Theorem necomi 2340

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 2339	. 2 ⊢ (𝐴 ≠ 𝐵 ↔ 𝐵 ≠ 𝐴)
3	1, 2	mpbi 143	1 ⊢ 𝐵 ≠ 𝐴

Syntax hints:   ≠ wne 2255

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-5 1381  ax-gen 1383  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-ne 2256

This theorem is referenced by:  0nep0  4000  xp01disj  6198  djulclb  6747  djuinr  6755  djuin  6756  pnfnemnf  7542  mnfnepnf  7543  ltneii  7581  1ne0  8490  0ne2  8621  fzprval  9496  0tonninf  9845  1tonninf  9846