Theorem necom 2484

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 2231	. 2 ⊢ (𝐴 = 𝐵 ↔ 𝐵 = 𝐴)
2	1	necon3bii 2438	1 ⊢ (𝐴 ≠ 𝐵 ↔ 𝐵 ≠ 𝐴)

Syntax hints:   ↔ wb 105   ≠ wne 2400

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 617  ax-in2 618  ax-5 1493  ax-gen 1495  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-ne 2401

This theorem is referenced by:  necomi  2485  necomd  2486  difprsn1  3810  difprsn2  3811  diftpsn3  3812  fndmdifcom  5749  fvpr1  5853  fvpr2  5854  fvpr1g  5855  fvtp1g  5857  fvtp2g  5858  fvtp3g  5859  fvtp2  5861  fvtp3  5862  netap  7466  2omotaplemap  7469  zltlen  9551  nn0lt2  9554  qltlen  9867  fzofzim  10420  flqeqceilz  10573  isprm2lem  12681  prm2orodd  12691  tridceq  16610