Theorem reseq1d

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

	Ref	Expression
Hypothesis	reseqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	reseq1d	⊢ ( 𝜑 → ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		reseqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		reseq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐶 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ↾ 𝐶 ) = ( 𝐵 ↾ 𝐶 ) )