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Theorem jao 533
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 pm3.44 532 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
21ex 449 1 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 382
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-an 385
This theorem is referenced by:  3jao  1429  suctrOLD  5847  en3lplem2  8550  indpi  9767  bj-orim2  32666  bj-currypeirce  32669  jaoded  39099  suctrALT2VD  39385  suctrALT2  39386  en3lplem2VD  39393  hbimpgVD  39454  ax6e2ndeqVD  39459  suctrALTcf  39472  suctrALTcfVD  39473  ax6e2ndeqALT  39481
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