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Metamath Proof Explorer

Theorem fneq12

Description: Equality theorem for function predicate with domain. (Contributed by Thierry Arnoux, 31-Jan-2017)

		Ref	Expression
	Assertion	fneq12	$⊢ (F = G \land A = B) \to (F Fn A \leftrightarrow G Fn B)$

Step	Hyp	Ref	Expression
1		simpl	$⊢ (F = G \land A = B) \to F = G$
2		simpr	$⊢ (F = G \land A = B) \to A = B$
3	1 2	fneq12d	$⊢ (F = G \land A = B) \to (F Fn A \leftrightarrow G Fn B)$