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Theorem ecase23d 1256
Description: Variation of ecased 1255 with three disjuncts instead of two. (Contributed by NM, 22-Apr-1994.) (Revised by Jim Kingdon, 9-Dec-2017.)
Hypotheses
Ref Expression
ecase23d.1 (𝜑 → ¬ 𝜒)
ecase23d.2 (𝜑 → ¬ 𝜃)
ecase23d.3 (𝜑 → (𝜓𝜒𝜃))
Assertion
Ref Expression
ecase23d (𝜑𝜓)

Proof of Theorem ecase23d
StepHypRef Expression
1 ecase23d.1 . 2 (𝜑 → ¬ 𝜒)
2 ecase23d.2 . . 3 (𝜑 → ¬ 𝜃)
3 ecase23d.3 . . . 4 (𝜑 → (𝜓𝜒𝜃))
4 df-3or 897 . . . 4 ((𝜓𝜒𝜃) ↔ ((𝜓𝜒) ∨ 𝜃))
53, 4sylib 131 . . 3 (𝜑 → ((𝜓𝜒) ∨ 𝜃))
62, 5ecased 1255 . 2 (𝜑 → (𝜓𝜒))
71, 6ecased 1255 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 639  w3o 895
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-3or 897
This theorem is referenced by: (None)
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