Theorem necom 2267

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 2024	. 2 ⊢ (A = B ↔ B = A)
2	1	necon3bii 2221	1 ⊢ (A ≠ B ↔ B ≠ A)

Syntax hints:   ↔ wb 98   ≠ wne 2186

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 532  ax-in2 533  ax-5 1316  ax-gen 1318  ax-ext 2004

This theorem depends on definitions:  df-bi 110  df-cleq 2015  df-ne 2188

This theorem is referenced by:  necomi  2268  necomd  2269  0pss  3242  difprsn1  3477  difprsn2  3478  diftpsn3  3479  fndmdifcom  5198  fvpr1  5290  fvpr2  5291  fvpr1g  5292  fvtp1g  5294  fvtp2g  5295  fvtp3g  5296  fvtp2  5298  fvtp3  5299