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

Theorem jao 671
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) → ((φ χ) → ψ)))

Proof of Theorem jao
StepHypRef Expression
1 pm3.44 634 . 2 (((φψ) (χψ)) → ((φ χ) → ψ))
21ex 108 1 ((φψ) → ((χψ) → ((φ χ) → ψ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  3jao  1195  suctr  4124
  Copyright terms: Public domain W3C validator