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Theorem simplimdc 768
Description: Simplification for a decidable proposition. Similar to Theorem *3.26 (Simp) of [WhiteheadRussell] p. 112. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
simplimdc (DECID 𝜑 → (¬ (𝜑𝜓) → 𝜑))

Proof of Theorem simplimdc
StepHypRef Expression
1 pm2.21 557 . 2 𝜑 → (𝜑𝜓))
2 con1dc 764 . 2 (DECID 𝜑 → ((¬ 𝜑 → (𝜑𝜓)) → (¬ (𝜑𝜓) → 𝜑)))
31, 2mpi 15 1 (DECID 𝜑 → (¬ (𝜑𝜓) → 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  DECID wdc 753
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-dc 754
This theorem is referenced by:  pm2.5dc  774  dfandc  789  pm4.79dc  820
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