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Metamath Proof Explorer

Theorem necon3i

Description: Contrapositive inference for inequality. (Contributed by NM, 9-Aug-2006) (Proof shortened by Wolf Lammen, 22-Nov-2019)

		Ref	Expression
	Hypothesis	necon3i.1	$⊢ A = B \to C = D$
	Assertion	necon3i	$⊢ C \neq D \to A \neq B$

Step	Hyp	Ref	Expression
1		necon3i.1	$⊢ A = B \to C = D$
2	1	necon3ai	$⊢ C \neq D \to \neg A = B$
3	2	neqned	$⊢ C \neq D \to A \neq B$