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Metamath Proof Explorer

Theorem reseq1d

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

		Ref	Expression
	Hypothesis	reseqd.1	$⊢ φ \to A = B$
	Assertion	reseq1d	$⊢ φ \to {A ↾}_{C} = {B ↾}_{C}$

Step	Hyp	Ref	Expression
1		reseqd.1	$⊢ φ \to A = B$
2		reseq1	$⊢ A = B \to {A ↾}_{C} = {B ↾}_{C}$
3	1 2	syl	$⊢ φ \to {A ↾}_{C} = {B ↾}_{C}$