Theorem pm1.5 508

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 374	. . 3 ⊢ (φ → (φ ∨ χ))
2	1	olcd 382	. 2 ⊢ (φ → (ψ ∨ (φ ∨ χ)))
3		olc 373	. . 3 ⊢ (χ → (φ ∨ χ))
4	3	orim2i 504	. 2 ⊢ ((ψ ∨ χ) → (ψ ∨ (φ ∨ χ)))
5	2, 4	jaoi 368	1 ⊢ ((φ ∨ (ψ ∨ χ)) → (ψ ∨ (φ ∨ χ)))

Syntax hints:   → wi 4   ∨ wo 357

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 177  df-or 359

This theorem is referenced by:  or12  509