Theorem necomi 2598

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 2597	. 2 ⊢ (A ≠ B ↔ B ≠ A)
3	1, 2	mpbi 199	1 ⊢ B ≠ A

Syntax hints:   ≠ wne 2516

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-cleq 2346  df-ne 2518

This theorem is referenced by:  necompl  3544  ltfinirr  4457  evenodddisj  4516  nfunv  5138  nnltp1c  6262