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Metamath Proof Explorer

Theorem necon3abii

Description: Deduction from equality to inequality. (Contributed by NM, 9-Nov-2007)

		Ref	Expression
	Hypothesis	necon3abii.1	$⊢ A = B \leftrightarrow φ$
	Assertion	necon3abii	$⊢ A \neq B \leftrightarrow \neg φ$

Step	Hyp	Ref	Expression
1		necon3abii.1	$⊢ A = B \leftrightarrow φ$
2		df-ne	$⊢ A \neq B \leftrightarrow \neg A = B$
3	2 1	xchbinx	$⊢ A \neq B \leftrightarrow \neg φ$