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Theorem con5 39045
Description: Biconditional contraposition variation. This proof is con5VD 39450 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
con5 ((𝜑 ↔ ¬ 𝜓) → (¬ 𝜑𝜓))

Proof of Theorem con5
StepHypRef Expression
1 biimpr 210 . 2 ((𝜑 ↔ ¬ 𝜓) → (¬ 𝜓𝜑))
21con1d 139 1 ((𝜑 ↔ ¬ 𝜓) → (¬ 𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196
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 197
This theorem is referenced by:  con5i  39046
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