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Theorem pm4.42r 915
Description: One direction of Theorem *4.42 of [WhiteheadRussell] p. 119. (Contributed by Jim Kingdon, 4-Aug-2018.)
Assertion
Ref Expression
pm4.42r (((𝜑𝜓) ∨ (𝜑 ∧ ¬ 𝜓)) → 𝜑)

Proof of Theorem pm4.42r
StepHypRef Expression
1 simpl 107 . 2 ((𝜑𝜓) → 𝜑)
2 simpl 107 . 2 ((𝜑 ∧ ¬ 𝜓) → 𝜑)
31, 2jaoi 669 1 (((𝜑𝜓) ∨ (𝜑 ∧ ¬ 𝜓)) → 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102  wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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