Theorem reseq2i

Description: Equality inference for restrictions. (Contributed by Paul Chapman, 22-Jun-2011)

	Ref	Expression
Hypothesis	reseqi.1	⊢ 𝐴 = 𝐵
Assertion	reseq2i	⊢ ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		reseqi.1	⊢ 𝐴 = 𝐵
2		reseq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 )