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Theorem jao 974
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 pm3.44 973 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
21ex 399 1 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 865
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 198  df-an 385  df-or 866
This theorem is referenced by:  3jao  1542  3jaoOLD  1543  suctrOLD  6016  en3lplem2  8749  indpi  10008  bj-orim2  32851  bj-currypeirce  32854  jaodd  37743  jaoded  39274  suctrALT2VD  39559  suctrALT2  39560  en3lplem2VD  39567  hbimpgVD  39628  ax6e2ndeqVD  39633  suctrALTcf  39646  suctrALTcfVD  39647  ax6e2ndeqALT  39655
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