Theorem pm1.5 933

Description: Axiom *1.5 (Assoc) of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm1.5	⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒)))

Proof of Theorem pm1.5

Step	Hyp	Ref	Expression
1		orc 881	. . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜒))
2	1	olcd 888	. 2 ⊢ (𝜑 → (𝜓 ∨ (𝜑 ∨ 𝜒)))
3		olc 882	. . 3 ⊢ (𝜒 → (𝜑 ∨ 𝜒))
4	3	orim2i 924	. 2 ⊢ ((𝜓 ∨ 𝜒) → (𝜓 ∨ (𝜑 ∨ 𝜒)))
5	2, 4	jaoi 871	1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  or12  934  meran1  37179  meran3  37181