Theorem reseq2d

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

	Ref	Expression
Hypothesis	reseqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	reseq2d	⊢ ( 𝜑 → ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		reseqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		reseq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐶 ↾ 𝐴 ) = ( 𝐶 ↾ 𝐵 ) )