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Theorem neqne 2257
Description: From non equality to inequality. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Assertion
Ref Expression
neqne 𝐴 = 𝐵𝐴𝐵)

Proof of Theorem neqne
StepHypRef Expression
1 id 19 . 2 𝐴 = 𝐵 → ¬ 𝐴 = 𝐵)
21neqned 2256 1 𝐴 = 𝐵𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1285  wne 2249
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-ne 2250
This theorem is referenced by:  dvdsabseq  10628
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