Theorem reseq1i

Description: Equality inference for restrictions. (Contributed by NM, 21-Oct-2014)

	Ref	Expression
Hypothesis	reseqi.1	⊢ 𝐴 = 𝐵
Assertion	reseq1i	⊢ ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		reseqi.1	⊢ 𝐴 = 𝐵
2		reseq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐶 )