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Theorem necon3abii 2363
Description: Deduction from equality to inequality. (Contributed by NM, 9-Nov-2007.)
Hypothesis
Ref Expression
necon3abii.1 (𝐴 = 𝐵𝜑)
Assertion
Ref Expression
necon3abii (𝐴𝐵 ↔ ¬ 𝜑)

Proof of Theorem necon3abii
StepHypRef Expression
1 df-ne 2328 . 2 (𝐴𝐵 ↔ ¬ 𝐴 = 𝐵)
2 necon3abii.1 . 2 (𝐴 = 𝐵𝜑)
31, 2xchbinx 672 1 (𝐴𝐵 ↔ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104   = wceq 1335  wne 2327
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116  df-ne 2328
This theorem is referenced by:  necon3bbii  2364  necon3bii  2365  nesym  2372  n0rf  3406  gcd0id  11867
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