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Theorem pm2.26dc 812
Description: Decidable proposition version of theorem *2.26 of [WhiteheadRussell] p. 104. (Contributed by Jim Kingdon, 20-Apr-2018.)
Assertion
Ref Expression
pm2.26dc (DECID φ → (¬ φ ((φψ) → ψ)))

Proof of Theorem pm2.26dc
StepHypRef Expression
1 pm2.27 35 . 2 (φ → ((φψ) → ψ))
2 imordc 795 . 2 (DECID φ → ((φ → ((φψ) → ψ)) ↔ (¬ φ ((φψ) → ψ))))
31, 2mpbii 136 1 (DECID φ → (¬ φ ((φψ) → ψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 628  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: (None)
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