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Theorem necon2bi 2254
Description: Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007.)
Hypothesis
Ref Expression
necon2bi.1 (φAB)
Assertion
Ref Expression
necon2bi (A = B → ¬ φ)

Proof of Theorem necon2bi
StepHypRef Expression
1 necon2bi.1 . . 3 (φAB)
21neneqd 2221 . 2 (φ → ¬ A = B)
32con2i 557 1 (A = B → ¬ φ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-ne 2203
This theorem is referenced by:  minel  3277  rzal  3312  difsnb  3497  0npi  6297  0nsr  6657  renfdisj  6856  nltpnft  8480  ngtmnft  8481  xrrebnd  8482  rennim  9191
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