Theorem necomi 2393

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 2392	. 2 ⊢ (𝐴 ≠ 𝐵 ↔ 𝐵 ≠ 𝐴)
3	1, 2	mpbi 144	1 ⊢ 𝐵 ≠ 𝐴

Syntax hints:   ≠ wne 2308

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-ne 2309

This theorem is referenced by:  0nep0  4089  xp01disj  6330  xp01disjl  6331  djulclb  6940  djuinr  6948  pnfnemnf  7820  mnfnepnf  7821  ltneii  7860  1ne0  8788  0ne2  8925  fzprval  9862  0tonninf  10212  1tonninf  10213