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The promises were given to Abraham. They were also given to his seed. Scripture does not say, "and to seeds." That means many people. It says, "and to your seed."--(Genesis 12:7; 13:15; 24:7) That means one person. And that one person is Christ.
Reference
Greek: ὁ (ho)
the (sometimes to be supplied, at others omitted, in English idiom)
Hebrew: ʼillêyn
these
Greek: Ἀβραάμ (Abraám)
Abraham, the Hebrew patriarch
Hebrew: ʼAbrâhâm
Abraham, the later name of Abram
Greek: δή (dḗ)
a particle of emphasis or explicitness; now, then, etc.
Hebrew: ʼôw
desire (and so probably in Proverbs 31:4); hence (by way of alternative) or, also if
Greek: τοῦ (toû)
sometimes used for G5127 (τούτου); of this person
Greek: σπορά (sporá)
a sowing, i.e. (by implication) parentage
Hebrew: zᵉraʻ
posterity
Greek: γραφή (graphḗ)
a document, i.e. holy Writ (or its contents or a statement in it)
Greek: οὐδαμῶς (oudamōs)
by no means
Hebrew: ʼîyn
is it not?
Greek: ἀποφθέγγομαι (apophthéngomai)
to enunciate plainly, i.e. declare
Hebrew: mâlal
to speak (mostly poetical) or say
Greek: καίγε (kaíge)
and at least (or even, indeed)
Hebrew: kîy
(by implication) very widely used as a relative conjunction or adverb (as below); often largely modified by other particles annexed
Hebrew: zôw
this or that
Hebrew: rᵉbâbâh
abundance (in number), i.e. (specifically) a myriad (whether definite or indefinite)
Greek: δῆμος (dēmos)
the public (as bound together socially)
Hebrew: ʻam
{a people (as a congregated unit); specifically, a tribe (as those of Israel); hence (collectively) troops or attendants; figuratively, a flock}
Hebrew: hêm
they (only used when emphatic)
Greek: καίγε (kaíge)
and at least (or even, indeed)
Hebrew: kîy
(by implication) very widely used as a relative conjunction or adverb (as below); often largely modified by other particles annexed
Greek: σπορά (sporá)
a sowing, i.e. (by implication) parentage
Hebrew: zᵉraʻ
posterity
Hebrew: zôw
this or that
Greek: εἰρήνη (eirḗnē)
peace (literally or figuratively); by implication, prosperity
Hebrew: ʼalmônîy
some one (i.e. so and so, without giving the name of the person or place)
Greek: καίγε (kaíge)
and at least (or even, indeed)
Hebrew: kîy
(by implication) very widely used as a relative conjunction or adverb (as below); often largely modified by other particles annexed
Hebrew: zôw
this or that
Greek: εἰρήνη (eirḗnē)
peace (literally or figuratively); by implication, prosperity
Hebrew: ʼalmônîy
some one (i.e. so and so, without giving the name of the person or place)
Greek: Χριστός (Christós)
anointed, i.e. the Messiah, an epithet of Jesus
Covenant
Romans 4:13
Romans 4:16
Acts 3:25
Parallel theme
Genesis 12:7
Genesis 12:3
Genesis 15:5
References Abraham
Luke 1:55
Galatians 3:8
Genesis 21:12
References Christ
Colossians 3:11
Verse Explanation
Paul explains that God's promises were spoken to Abraham and to his offspring, ultimately pointing to Christ, showing that the promise reaches its fulfillment through Jesus rather than through every descendant collectively.
History
Old Testament background: The Abrahamic promises appear throughout Genesis, long before the Mosaic law was given.