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  3806  difprsn2  3807  diftpsn3  3808  fndmdifcom  5734  fvpr1  5836  fvpr2  5837  fvpr1g  5838  fvtp1g  5840  fvtp2g  5841  fvtp3g  5842  fvtp2  5844  fvtp3  5845  netap  7428  2omotaplemap  7431  zltlen  9513  nn0lt2  9516  qltlen  9823  fzofzim  10376  flqeqceilz  10527  isprm2lem  12624  prm2orodd  12634  tridceq  16355