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Theorem orfa2 34218
Description: Remove a contradicting disjunct from an antecedent. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Hypothesis
Ref Expression
orfa2.1 (𝜑 → ⊥)
Assertion
Ref Expression
orfa2 ((𝜑𝜓) → 𝜓)

Proof of Theorem orfa2
StepHypRef Expression
1 orfa2.1 . . 3 (𝜑 → ⊥)
21orim1i 540 . 2 ((𝜑𝜓) → (⊥ ∨ 𝜓))
3 falim 1647 . . 3 (⊥ → 𝜓)
4 id 22 . . 3 (𝜓𝜓)
53, 4jaoi 393 . 2 ((⊥ ∨ 𝜓) → 𝜓)
62, 5syl 17 1 ((𝜑𝜓) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382  wfal 1637
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-tru 1635  df-fal 1638
This theorem is referenced by: (None)
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