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Theorem jao 958
 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 pm3.44 957 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
21ex 416 1 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 844 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 210  df-an 400  df-or 845 This theorem is referenced by:  3jao  1422  en3lplem2  9063  indpi  10321  bj-orim2  34023  jaodd  39409  jaoded  41315  suctrALT2VD  41585  suctrALT2  41586  en3lplem2VD  41593  hbimpgVD  41653  ax6e2ndeqVD  41658  suctrALTcf  41671  suctrALTcfVD  41672  ax6e2ndeqALT  41680
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