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Theorem necon1d 2585
Description: Contrapositive law deduction for inequality. (Contributed by NM, 28-Dec-2008.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
necon1d.1 (φ → (ABC = D))
Assertion
Ref Expression
necon1d (φ → (CDA = B))

Proof of Theorem necon1d
StepHypRef Expression
1 necon1d.1 . . 3 (φ → (ABC = D))
2 nne 2520 . . 3 CDC = D)
31, 2syl6ibr 218 . 2 (φ → (AB → ¬ CD))
43necon4ad 2577 1 (φ → (CDA = B))
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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