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Theorem ecase3ad 985
Description: Deduction for elimination by cases. (Contributed by NM, 24-May-2013.)
Hypotheses
Ref Expression
ecase3ad.1 (𝜑 → (𝜓𝜃))
ecase3ad.2 (𝜑 → (𝜒𝜃))
ecase3ad.3 (𝜑 → ((¬ 𝜓 ∧ ¬ 𝜒) → 𝜃))
Assertion
Ref Expression
ecase3ad (𝜑𝜃)

Proof of Theorem ecase3ad
StepHypRef Expression
1 notnotr 125 . . 3 (¬ ¬ 𝜓𝜓)
2 ecase3ad.1 . . 3 (𝜑 → (𝜓𝜃))
31, 2syl5 34 . 2 (𝜑 → (¬ ¬ 𝜓𝜃))
4 notnotr 125 . . 3 (¬ ¬ 𝜒𝜒)
5 ecase3ad.2 . . 3 (𝜑 → (𝜒𝜃))
64, 5syl5 34 . 2 (𝜑 → (¬ ¬ 𝜒𝜃))
7 ecase3ad.3 . 2 (𝜑 → ((¬ 𝜓 ∧ ¬ 𝜒) → 𝜃))
83, 6, 7ecased 984 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 384
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 197  df-or 385  df-an 386
This theorem is referenced by: (None)
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