Theorem necomi 2334

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 2333	. 2 |- ( A =/= B <-> B =/= A )
3	1, 2	mpbi 143	1 |- B =/= A

Syntax hints:   =/= wne 2249

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 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250

This theorem is referenced by:  0nep0  3959  xp01disj  6102  djuin  6562  pnfnemnf  7305  mnfnepnf  7306  ltneii  7344  1ne0  8244  0ne2  8374  fzprval  9245