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Theorem 3o2cs 29619
Description: Deduction eliminating disjunct. (Contributed by Thierry Arnoux, 19-Dec-2016.)
Hypothesis
Ref Expression
3o1cs.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3o2cs (𝜓𝜃)

Proof of Theorem 3o2cs
StepHypRef Expression
1 df-3or 1073 . . . 4 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
2 3o1cs.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
31, 2sylbir 225 . . 3 (((𝜑𝜓) ∨ 𝜒) → 𝜃)
43orcs 408 . 2 ((𝜑𝜓) → 𝜃)
54olcs 409 1 (𝜓𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382  w3o 1071
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 384  df-3or 1073
This theorem is referenced by:  xrpxdivcld  29952
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