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Theorem pm5.14dc 805
Description: A decidable proposition is implied by or implies other propositions. Based on theorem *5.14 of [WhiteheadRussell] p. 123. (Contributed by Jim Kingdon, 30-Mar-2018.)
Assertion
Ref Expression
pm5.14dc (DECID ψ → ((φψ) (ψχ)))

Proof of Theorem pm5.14dc
StepHypRef Expression
1 df-dc 715 . 2 (DECID ψ ↔ (ψ ¬ ψ))
2 ax-1 5 . . 3 (ψ → (φψ))
3 ax-in2 527 . . 3 ψ → (ψχ))
42, 3orim12i 651 . 2 ((ψ ¬ ψ) → ((φψ) (ψχ)))
51, 4sylbi 112 1 (DECID ψ → ((φψ) (ψχ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wo 605  DECID wdc 714
This theorem is referenced by:  pm5.13dc  806
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-in2 527  ax-io 606
This theorem depends on definitions:  df-bi 108  df-dc 715
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