This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fneq2d

Description: Equality deduction for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011)

		Ref	Expression
	Hypothesis	fneq2d.1	$⊢ φ \to A = B$
	Assertion	fneq2d	$⊢ φ \to (F Fn A \leftrightarrow F Fn B)$

Step	Hyp	Ref	Expression
1		fneq2d.1	$⊢ φ \to A = B$
2		fneq2	$⊢ A = B \to (F Fn A \leftrightarrow F Fn B)$
3	1 2	syl	$⊢ φ \to (F Fn A \leftrightarrow F Fn B)$