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  3807  difprsn2  3808  diftpsn3  3809  fndmdifcom  5746  fvpr1  5850  fvpr2  5851  fvpr1g  5852  fvtp1g  5854  fvtp2g  5855  fvtp3g  5856  fvtp2  5858  fvtp3  5859  netap  7456  2omotaplemap  7459  zltlen  9541  nn0lt2  9544  qltlen  9852  fzofzim  10405  flqeqceilz  10557  isprm2lem  12659  prm2orodd  12669  tridceq  16538