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Metamath Proof Explorer

Theorem pm1.5

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

Ref Expression
Assertion pm1.5 ⊢ φ ∨ ψ ∨ χ → ψ ∨ φ ∨ χ

Proof

Step Hyp Ref Expression
1 orc ⊢ φ → φ ∨ χ
2 1 olcd ⊢ φ → ψ ∨ φ ∨ χ
3 olc ⊢ χ → φ ∨ χ
4 3 orim2i ⊢ ψ ∨ χ → ψ ∨ φ ∨ χ
5 2 4 jaoi ⊢ φ ∨ ψ ∨ χ → ψ ∨ φ ∨ χ