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  10703  1tonninf  10704  ressplusgd  13230  ressmulrg  13246  fnpr2o  13440  fvpr0o  13442  fvpr1o  13443  mgpress  13963  rmodislmod  14384  sralemg  14471  srascag  14475  sratsetg  14478  sradsg  14481  zlmbasg  14662  zlmplusgg  14663  zlmmulrg  14664  zlmsca  14665  znbas2  14673  znadd  14674  znmul  14675  usgrexmpldifpr  16119  konigsbergiedgwen  16354  konigsberglem2  16359  konigsberglem3  16360  konigsberglem5  16362