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Theorem pm2.5dc 762
Description: Negating an implication for a decidable antecedent. Based on theorem *2.5 of [WhiteheadRussell] p. 107. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
pm2.5dc (DECID φ → (¬ (φψ) → (¬ φψ)))

Proof of Theorem pm2.5dc
StepHypRef Expression
1 simplimdc 756 . . . 4 (DECID φ → (¬ (φψ) → φ))
21imp 115 . . 3 ((DECID φ ¬ (φψ)) → φ)
32pm2.24d 552 . 2 ((DECID φ ¬ (φψ)) → (¬ φψ))
43ex 108 1 (DECID φ → (¬ (φψ) → (¬ φψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97  DECID wdc 741
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 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  pm5.11dc  814
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