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Theorem jaob 817
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 pm2.67-2 415 . . 3 (((𝜑𝜒) → 𝜓) → (𝜑𝜓))
2 olc 397 . . . 4 (𝜒 → (𝜑𝜒))
32imim1i 60 . . 3 (((𝜑𝜒) → 𝜓) → (𝜒𝜓))
41, 3jca 552 . 2 (((𝜑𝜒) → 𝜓) → ((𝜑𝜓) ∧ (𝜒𝜓)))
5 pm3.44 531 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
64, 5impbii 197 1 (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wo 381  wa 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 195  df-or 383  df-an 384
This theorem is referenced by:  pm4.77  823  pm5.53  832  pm4.83  965  axio  2579  unss  3748  ralunb  3755  intun  4438  intpr  4439  relop  5182  sqrt2irr  14763  algcvgblem  15074  efgred  17930  caucfil  22807  plydivex  23773  2sqlem6  24865  arg-ax  31391  tendoeq2  34876  ifpidg  36651
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