Theorem necomi 2290

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 2289	. 2 ⊢ (𝐴 ≠ 𝐵 ↔ 𝐵 ≠ 𝐴)
3	1, 2	mpbi 133	1 ⊢ 𝐵 ≠ 𝐴

Syntax hints:   ≠ wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206

This theorem is referenced by:  0nep0  3918  xp01disj  6017  ltneii  7114  1ne0  7983  0ne2  8131  pnfnemnf  8697  mnfnepnf  8698  fzprval  8944