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Theorem neneq 2268
Description: From inequality to non equality. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Assertion
Ref Expression
neneq (𝐴𝐵 → ¬ 𝐴 = 𝐵)

Proof of Theorem neneq
StepHypRef Expression
1 id 19 . 2 (𝐴𝐵𝐴𝐵)
21neneqd 2267 1 (𝐴𝐵 → ¬ 𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1285  wne 2246
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104
This theorem depends on definitions:  df-bi 115  df-ne 2247
This theorem is referenced by:  gcd2n0cl  10505
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