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

Metamath Proof Explorer

Theorem necomi

Description: Inference from commutative law for inequality. (Contributed by NM, 17-Oct-2012)

		Ref	Expression
	Hypothesis	necomi.1	$⊢ A \neq B$
	Assertion	necomi	$⊢ B \neq A$

Step	Hyp	Ref	Expression
1		necomi.1	$⊢ A \neq B$
2		necom	$⊢ A \neq B \leftrightarrow B \neq A$
3	1 2	mpbi	$⊢ B \neq A$