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Theorem pm1.5 542
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 398 . . 3 (𝜑 → (𝜑𝜒))
21olcd 406 . 2 (𝜑 → (𝜓 ∨ (𝜑𝜒)))
3 olc 397 . . 3 (𝜒 → (𝜑𝜒))
43orim2i 538 . 2 ((𝜓𝜒) → (𝜓 ∨ (𝜑𝜒)))
52, 4jaoi 392 1 ((𝜑 ∨ (𝜓𝜒)) → (𝜓 ∨ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381
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
This theorem is referenced by:  or12  543  meran1  31414  meran3  31416
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