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Metamath Proof Explorer

Theorem necon1i

Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007)

		Ref	Expression
	Hypothesis	necon1i.1	$⊢ A \neq B \to C = D$
	Assertion	necon1i	$⊢ C \neq D \to A = B$

Step	Hyp	Ref	Expression
1		necon1i.1	$⊢ A \neq B \to C = D$
2		df-ne	$⊢ A \neq B \leftrightarrow \neg A = B$
3	2 1	sylbir	$⊢ \neg A = B \to C = D$
4	3	necon1ai	$⊢ C \neq D \to A = B$