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Theorem con2biidc 817
Description: A contraposition inference. (Contributed by Jim Kingdon, 15-Mar-2018.)
Hypothesis
Ref Expression
con2biidc.1 (DECID 𝜓 → (𝜑 ↔ ¬ 𝜓))
Assertion
Ref Expression
con2biidc (DECID 𝜓 → (𝜓 ↔ ¬ 𝜑))

Proof of Theorem con2biidc
StepHypRef Expression
1 con2biidc.1 . . . 4 (DECID 𝜓 → (𝜑 ↔ ¬ 𝜓))
21bicomd 140 . . 3 (DECID 𝜓 → (¬ 𝜓𝜑))
32con1biidc 815 . 2 (DECID 𝜓 → (¬ 𝜑𝜓))
43bicomd 140 1 (DECID 𝜓 → (𝜓 ↔ ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 104  DECID wdc 786
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671
This theorem depends on definitions:  df-bi 116  df-dc 787
This theorem is referenced by:  dfexdc  1445  nnedc  2272
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