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Theorem jaob 964
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 pm2.67-2 892 . . 3 (((𝜑𝜒) → 𝜓) → (𝜑𝜓))
2 olc 869 . . . 4 (𝜒 → (𝜑𝜒))
32imim1i 63 . . 3 (((𝜑𝜒) → 𝜓) → (𝜒𝜓))
41, 3jca 511 . 2 (((𝜑𝜒) → 𝜓) → ((𝜑𝜓) ∧ (𝜒𝜓)))
5 pm3.44 962 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
64, 5impbii 209 1 (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wa 395  wo 848
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 207  df-an 396  df-or 849
This theorem is referenced by:  pm4.77  965  pm5.53  1007  pm4.83  1027  axio  2698  elunant  4184  intprg  4981  relop  5861  sqrt2irr  16285  algcvgblem  16614  efgred  19766  caucfil  25317  plydivex  26339  2sqlem6  27467  arg-ax  36417  tendoeq2  40776  ifpidg  43504
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