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Theorem jao 534
Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)
Assertion
Ref Expression
jao ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))

Proof of Theorem jao
StepHypRef Expression
1 pm3.44 533 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
21ex 450 1 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 383
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:  3jao  1388  suctrOLD  5807  en3lplem2  8509  indpi  9726  bj-orim2  32525  bj-currypeirce  32528  jaoded  38608  suctrALT2VD  38897  suctrALT2  38898  en3lplem2VD  38905  hbimpgVD  38966  ax6e2ndeqVD  38971  suctrALTcf  38984  suctrALTcfVD  38985  ax6e2ndeqALT  38993
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