Theorem necomi 2487

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 2486	. 2 |- ( A =/= B <-> B =/= A )
3	1, 2	mpbi 145	1 |- B =/= A

Syntax hints:   =/= wne 2402

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-5 1495  ax-gen 1497  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-ne 2403

This theorem is referenced by:  0nep0  4255  xp01disj  6601  xp01disjl  6602  rex2dom  6996  djulclb  7254  djuinr  7262  2oneel  7475  pnfnemnf  8234  mnfnepnf  8235  ltneii  8276  1ne0  9211  0ne2  9349  fzprval  10317  0tonninf  10702  1tonninf  10703  ressplusgd  13213  ressmulrg  13229  fnpr2o  13423  fvpr0o  13425  fvpr1o  13426  mgpress  13946  rmodislmod  14367  sralemg  14454  srascag  14458  sratsetg  14461  sradsg  14464  zlmbasg  14645  zlmplusgg  14646  zlmmulrg  14647  zlmsca  14648  znbas2  14656  znadd  14657  znmul  14658  usgrexmpldifpr  16102