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Theorem jao 959
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 pm3.44 958 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
21ex 412 1 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 846
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 206  df-an 396  df-or 847
This theorem is referenced by:  3jao  1423  en3lplem2  9630  indpi  10924  bj-orim2  36021  jaodd  41668  jaoded  43977  suctrALT2VD  44247  suctrALT2  44248  en3lplem2VD  44255  hbimpgVD  44315  ax6e2ndeqVD  44320  suctrALTcf  44333  suctrALTcfVD  44334  ax6e2ndeqALT  44342
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