Theorem necomi 2412

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 2411	. 2 |- ( A =/= B <-> B =/= A )
3	1, 2	mpbi 144	1 |- B =/= A

Syntax hints:   =/= wne 2327

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1427  ax-gen 1429  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-cleq 2150  df-ne 2328

This theorem is referenced by:  0nep0  4127  xp01disj  6381  xp01disjl  6382  djulclb  7000  djuinr  7008  pnfnemnf  7933  mnfnepnf  7934  ltneii  7974  1ne0  8902  0ne2  9039  fzprval  9985  0tonninf  10342  1tonninf  10343