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Theorem necon2d 2566
Description: Contrapositive inference for inequality. (Contributed by NM, 28-Dec-2008.)
Hypothesis
Ref Expression
necon2d.1 (φ → (A = BCD))
Assertion
Ref Expression
necon2d (φ → (C = DAB))

Proof of Theorem necon2d
StepHypRef Expression
1 necon2d.1 . . 3 (φ → (A = BCD))
2 df-ne 2518 . . 3 (CD ↔ ¬ C = D)
31, 2syl6ib 217 . 2 (φ → (A = B → ¬ C = D))
43necon2ad 2564 1 (φ → (C = DAB))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = 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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