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Theorem pm2.64 791
Description: Theorem *2.64 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.64 ((𝜑𝜓) → ((𝜑 ∨ ¬ 𝜓) → 𝜑))

Proof of Theorem pm2.64
StepHypRef Expression
1 ax-1 6 . . 3 (𝜑 → ((𝜑𝜓) → 𝜑))
2 orel2 716 . . 3 𝜓 → ((𝜑𝜓) → 𝜑))
31, 2jaoi 706 . 2 ((𝜑 ∨ ¬ 𝜓) → ((𝜑𝜓) → 𝜑))
43com12 30 1 ((𝜑𝜓) → ((𝜑 ∨ ¬ 𝜓) → 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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