MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm1.5 Structured version   Visualization version   GIF version

Theorem pm1.5 944
Description: Axiom *1.5 (Assoc) of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm1.5 ((𝜑 ∨ (𝜓𝜒)) → (𝜓 ∨ (𝜑𝜒)))

Proof of Theorem pm1.5
StepHypRef Expression
1 orc 894 . . 3 (𝜑 → (𝜑𝜒))
21olcd 901 . 2 (𝜑 → (𝜓 ∨ (𝜑𝜒)))
3 olc 895 . . 3 (𝜒 → (𝜑𝜒))
43orim2i 935 . 2 ((𝜓𝜒) → (𝜓 ∨ (𝜑𝜒)))
52, 4jaoi 884 1 ((𝜑 ∨ (𝜓𝜒)) → (𝜓 ∨ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 874
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 199  df-or 875
This theorem is referenced by:  or12  945  meran1  32918  meran3  32920
  Copyright terms: Public domain W3C validator