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Theorem necon3abii 2235
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 2203 . 2 (AB ↔ ¬ A = B)
2 necon3abii.1 . 2 (A = Bφ)
31, 2xchbinx 606 1 (AB ↔ ¬ φ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-ne 2203
This theorem is referenced by:  necon3bbii  2236  necon3bii  2237  nesym  2244  n0rf  3227
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