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Theorem necon2abid 2573
Description: Contrapositive deduction for inequality. (Contributed by NM, 18-Jul-2007.)
Hypothesis
Ref Expression
necon2abid.1 (φ → (A = B ↔ ¬ ψ))
Assertion
Ref Expression
necon2abid (φ → (ψAB))

Proof of Theorem necon2abid
StepHypRef Expression
1 necon2abid.1 . . 3 (φ → (A = B ↔ ¬ ψ))
21con2bid 319 . 2 (φ → (ψ ↔ ¬ A = B))
3 df-ne 2518 . 2 (AB ↔ ¬ A = B)
42, 3syl6bbr 254 1 (φ → (ψAB))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   = wceq 1642  wne 2516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-ne 2518
This theorem is referenced by: (None)
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