Theorem neneq 2425

Description: From inequality to non-equality. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Assertion

Ref	Expression
neneq	⊢ (𝐴 ≠ 𝐵 → ¬ 𝐴 = 𝐵)

Proof of Theorem neneq

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝐴 ≠ 𝐵 → 𝐴 ≠ 𝐵)
2	1	neneqd 2424	1 ⊢ (𝐴 ≠ 𝐵 → ¬ 𝐴 = 𝐵)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1398   ≠ wne 2403

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This theorem depends on definitions:  df-bi 117  df-ne 2404

This theorem is referenced by:  mpodifsnif  6124  gcd2n0cl  12620  isnsgrp  13569  lgsabs1  15858  structiedg0val  15981  umgr2edgneu  16153