Theorem pm1.5 765

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 712	. . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜒))
2	1	olcd 734	. 2 ⊢ (𝜑 → (𝜓 ∨ (𝜑 ∨ 𝜒)))
3		olc 711	. . 3 ⊢ (𝜒 → (𝜑 ∨ 𝜒))
4	3	orim2i 761	. 2 ⊢ ((𝜓 ∨ 𝜒) → (𝜓 ∨ (𝜑 ∨ 𝜒)))
5	2, 4	jaoi 716	1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  or12  766