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Theorem imorri 701
Description: Infer implication from disjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
imorri.1 𝜑𝜓)
Assertion
Ref Expression
imorri (𝜑𝜓)

Proof of Theorem imorri
StepHypRef Expression
1 imorri.1 . 2 𝜑𝜓)
2 pm2.21 580 . . 3 𝜑 → (𝜑𝜓))
3 ax-1 5 . . 3 (𝜓 → (𝜑𝜓))
42, 3jaoi 669 . 2 ((¬ 𝜑𝜓) → (𝜑𝜓))
51, 4ax-mp 7 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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