Theorem nesymi 2839

Description: Inference associated with nesym 2838. (Contributed by BJ, 7-Jul-2018.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)

Hypothesis

Ref	Expression
nesymi.1	⊢ 𝐴 ≠ 𝐵

Assertion

Ref	Expression
nesymi	⊢ ¬ 𝐵 = 𝐴

Proof of Theorem nesymi

Step	Hyp	Ref	Expression
1		nesymi.1	. . 3 ⊢ 𝐴 ≠ 𝐵
2	1	necomi 2836	. 2 ⊢ 𝐵 ≠ 𝐴
3	2	neii 2784	1 ⊢ ¬ 𝐵 = 𝐴

Syntax hints:  ¬ wn 3   = wceq 1475   ≠ wne 2780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-cleq 2603  df-ne 2782

This theorem is referenced by:  0nelxp  5067  recgt0ii  10808  xrltnr  11829  nltmnf  11839  xnn0xadd0  11949  setcepi  16561  pmtrprfval  17730  pmtrprfvalrn  17731  zringndrg  19657  vieta1lem2  23870  2lgslem3  24929  2lgslem4  24931  structiedg0val  25699  snstriedgval  25713  usgraedgprv  25905  2trllemA  26080  2pthon  26132  2pthon3v  26134  4cycl4dv  26195  rusgranumwlkl1  26474  frgrareggt1  26643  ballotlemi1  29891  sgnnbi  29934  sgnpbi  29935  plymulx0  29950  sltval2  31053  nosgnn0  31055  bj-0nel1  32133  bj-0nelsngl  32152  bj-pr22val  32200  bj-pinftynminfty  32291  finxp0  32404  wepwsolem  36630  refsum2cnlem1  38219  oddprmALTV  40136  rusgrnumwwlkl1  41172  av-frgrareggt1  41547