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Theorem pm2.74 754
Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm2.74 ((𝜓𝜑) → (((𝜑𝜓) ∨ 𝜒) → (𝜑𝜒)))

Proof of Theorem pm2.74
StepHypRef Expression
1 idd 21 . . 3 ((𝜓𝜑) → (𝜑𝜑))
2 id 19 . . 3 ((𝜓𝜑) → (𝜓𝜑))
31, 2jaod 670 . 2 ((𝜓𝜑) → ((𝜑𝜓) → 𝜑))
43orim1d 734 1 ((𝜓𝜑) → (((𝜑𝜓) ∨ 𝜒) → (𝜑𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  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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