Theorem necomi 2599

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

Hypothesis

Ref	Expression
necomi.1	|- A =/= B

Assertion

Ref	Expression
necomi	|- B =/= A

Proof of Theorem necomi

Step	Hyp	Ref	Expression
1		necomi.1	. 2 |- A =/= B
2		necom 2598	. 2 |- (A =/= B <-> B =/= A)
3	1, 2	mpbi 199	1 |- B =/= A

Syntax hints:   =/= wne 2517

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-cleq 2346  df-ne 2519

This theorem is referenced by:  necompl  3545  ltfinirr  4458  evenodddisj  4517  nfunv  5139  nnltp1c  6263