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Theorem pm2.6dc 758
Description: Case elimination for a decidable proposition. Based on theorem *2.6 of [WhiteheadRussell] p. 107. (Contributed by Jim Kingdon, 25-Mar-2018.)
Assertion
Ref Expression
pm2.6dc (DECID φ → ((¬ φψ) → ((φψ) → ψ)))

Proof of Theorem pm2.6dc
StepHypRef Expression
1 pm2.1dc 744 . . 3 (DECID φ → (¬ φ φ))
2 pm3.44 634 . . 3 (((¬ φψ) (φψ)) → ((¬ φ φ) → ψ))
31, 2syl5com 26 . 2 (DECID φ → (((¬ φψ) (φψ)) → ψ))
43expd 245 1 (DECID φ → ((¬ φψ) → ((φψ) → ψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97   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-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by:  jadc  759  jaddc  760  pm2.61dc  761
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