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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 ) ) )