Theorem necomi 2330

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 2329	. 2 |- ( A =/= B <-> B =/= A )
3	1, 2	mpbi 143	1 |- B =/= A

Syntax hints:   =/= wne 2245

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-ne 2246

This theorem is referenced by:  0nep0  3939  xp01disj  6040  ltneii  7207  1ne0  8107  0ne2  8237  pnfnemnf  8851  mnfnepnf  8852  fzprval  9099