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Theorem 3jaodd 30850
 Description: Double deduction form of 3jaoi 1383. (Contributed by Scott Fenton, 20-Apr-2011.)
Hypotheses
Ref Expression
3jaodd.1 (𝜑 → (𝜓 → (𝜒𝜂)))
3jaodd.2 (𝜑 → (𝜓 → (𝜃𝜂)))
3jaodd.3 (𝜑 → (𝜓 → (𝜏𝜂)))
Assertion
Ref Expression
3jaodd (𝜑 → (𝜓 → ((𝜒𝜃𝜏) → 𝜂)))

Proof of Theorem 3jaodd
StepHypRef Expression
1 3jaodd.1 . . . 4 (𝜑 → (𝜓 → (𝜒𝜂)))
21com3r 85 . . 3 (𝜒 → (𝜑 → (𝜓𝜂)))
3 3jaodd.2 . . . 4 (𝜑 → (𝜓 → (𝜃𝜂)))
43com3r 85 . . 3 (𝜃 → (𝜑 → (𝜓𝜂)))
5 3jaodd.3 . . . 4 (𝜑 → (𝜓 → (𝜏𝜂)))
65com3r 85 . . 3 (𝜏 → (𝜑 → (𝜓𝜂)))
72, 4, 63jaoi 1383 . 2 ((𝜒𝜃𝜏) → (𝜑 → (𝜓𝜂)))
87com3l 87 1 (𝜑 → (𝜓 → ((𝜒𝜃𝜏) → 𝜂)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ w3o 1030 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3or 1032  df-3an 1033 This theorem is referenced by: (None)
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