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Theorem jaob 959
 Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-May-1994.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)
Assertion
Ref Expression
jaob (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))

Proof of Theorem jaob
StepHypRef Expression
1 pm2.67-2 889 . . 3 (((𝜑𝜒) → 𝜓) → (𝜑𝜓))
2 olc 865 . . . 4 (𝜒 → (𝜑𝜒))
32imim1i 63 . . 3 (((𝜑𝜒) → 𝜓) → (𝜒𝜓))
41, 3jca 515 . 2 (((𝜑𝜒) → 𝜓) → ((𝜑𝜓) ∧ (𝜒𝜓)))
5 pm3.44 957 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
64, 5impbii 212 1 (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   ∧ wa 399   ∨ 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:  pm4.77  960  pm5.53  1002  pm4.83  1022  axio  2760  elunant  4105  intpr  4871  relop  5685  sqrt2irr  15596  algcvgblem  15913  efgred  18869  caucfil  23894  plydivex  24900  2sqlem6  26014  arg-ax  33889  tendoeq2  38086  ifpidg  40214
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