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

Metamath Proof Explorer

Theorem neneqd

Description: Deduction eliminating inequality definition. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

		Ref	Expression
	Hypothesis	neneqd.1	$⊢ φ \to A \neq B$
	Assertion	neneqd	$⊢ φ \to \neg A = B$

Step	Hyp	Ref	Expression
1		neneqd.1	$⊢ φ \to A \neq B$
2		df-ne	$⊢ A \neq B \leftrightarrow \neg A = B$
3	1 2	sylib	$⊢ φ \to \neg A = B$