ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  jaob GIF version

Theorem jaob 641
Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 640. (Contributed by NM, 30-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
jaob (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))

Proof of Theorem jaob
StepHypRef Expression
1 ax-io 640 1 (((𝜑𝜒) → 𝜓) ↔ ((𝜑𝜓) ∧ (𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102  wo 639
This theorem was proved from axioms:  ax-io 640
This theorem is referenced by:  olc  642  orc  643  pm3.44  645  pm4.77  723  pm5.53  726  unss  3144  ralunb  3151  intun  3673  intpr  3674  relop  4513  indstr  8631  sqrt2irr  10230  algcvgblem  10250  bj-inf2vnlem1  10461
  Copyright terms: Public domain W3C validator