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Theorem pm5.11dc 814
Description: A decidable proposition or its negation implies a second proposition. Based on theorem *5.11 of [WhiteheadRussell] p. 123. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
pm5.11dc (DECID φ → (DECID ψ → ((φψ) φψ))))

Proof of Theorem pm5.11dc
StepHypRef Expression
1 dcim 783 . 2 (DECID φ → (DECID ψDECID (φψ)))
2 pm2.5dc 762 . . 3 (DECID φ → (¬ (φψ) → (¬ φψ)))
3 pm2.54dc 789 . . 3 (DECID (φψ) → ((¬ (φψ) → (¬ φψ)) → ((φψ) φψ))))
42, 3syl5com 26 . 2 (DECID φ → (DECID (φψ) → ((φψ) φψ))))
51, 4syld 40 1 (DECID φ → (DECID ψ → ((φψ) φψ))))
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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