Theorem neneq 2358

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 2357	1 ⊢ (𝐴 ≠ 𝐵 → ¬ 𝐴 = 𝐵)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1343   ≠ wne 2336

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-ne 2337

This theorem is referenced by:  mpodifsnif  5935  gcd2n0cl  11902  lgsabs1  13580