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Theorem con1biddc 781
Description: A contraposition deduction. (Contributed by Jim Kingdon, 4-Apr-2018.)
Hypothesis
Ref Expression
con1biddc.1 (𝜑 → (DECID 𝜓 → (¬ 𝜓𝜒)))
Assertion
Ref Expression
con1biddc (𝜑 → (DECID 𝜓 → (¬ 𝜒𝜓)))

Proof of Theorem con1biddc
StepHypRef Expression
1 con1biddc.1 . 2 (𝜑 → (DECID 𝜓 → (¬ 𝜓𝜒)))
2 con1biimdc 778 . 2 (DECID 𝜓 → ((¬ 𝜓𝜒) → (¬ 𝜒𝜓)))
31, 2sylcom 28 1 (𝜑 → (DECID 𝜓 → (¬ 𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 102  DECID wdc 753
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-dc 754
This theorem is referenced by:  con2biddc  785  pm5.18dc  788  necon1abiddc  2282  necon1bbiddc  2283
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