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Theorem necon3abii 2256
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 2221 . 2 (𝐴𝐵 ↔ ¬ 𝐴 = 𝐵)
2 necon3abii.1 . 2 (𝐴 = 𝐵𝜑)
31, 2xchbinx 617 1 (𝐴𝐵 ↔ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 102   = wceq 1259  wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-ne 2221
This theorem is referenced by:  necon3bbii  2257  necon3bii  2258  nesym  2265  n0rf  3261
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