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Theorem con34bdc 753
Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116, but for a decidable proposition. (Contributed by Jim Kingdon, 24-Apr-2018.)
Assertion
Ref Expression
con34bdc (DECID ψ → ((φψ) ↔ (¬ ψ → ¬ φ)))

Proof of Theorem con34bdc
StepHypRef Expression
1 con3 558 . 2 ((φψ) → (¬ ψ → ¬ φ))
2 condc 737 . 2 (DECID ψ → ((¬ ψ → ¬ φ) → (φψ)))
31, 2impbid2 131 1 (DECID ψ → ((φψ) ↔ (¬ ψ → ¬ φ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98  DECID wdc 730
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 532  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110  df-dc 731
This theorem is referenced by:  pm4.14dc  775
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