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Metamath Proof Explorer

Theorem necon2bi

Description: Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007)

		Ref	Expression
	Hypothesis	necon2bi.1	$⊢ φ \to A \neq B$
	Assertion	necon2bi	$⊢ A = B \to \neg φ$

Step	Hyp	Ref	Expression
1		necon2bi.1	$⊢ φ \to A \neq B$
2	1	neneqd	$⊢ φ \to \neg A = B$
3	2	con2i	$⊢ A = B \to \neg φ$