Theorem necom 2597

Description: Commutation of inequality. (Contributed by NM, 14-May-1999.)

Assertion

Ref	Expression
necom	⊢ (A ≠ B ↔ B ≠ A)

Proof of Theorem necom

Step	Hyp	Ref	Expression
1		eqcom 2355	. 2 ⊢ (A = B ↔ B = A)
2	1	necon3bii 2548	1 ⊢ (A ≠ B ↔ B ≠ A)

Syntax hints:   ↔ wb 176   ≠ 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:  necomi  2598  necomd  2599  0pss  3588  difprsn1  3847  difprsn2  3848  diftpsn3  3849  fvpr1  5449  fvpr2  5450