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Metamath Proof Explorer

Theorem or32

Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995) (Proof shortened by Andrew Salmon, 26-Jun-2011)

Ref Expression
Assertion or32 ⊢ φ ∨ ψ ∨ χ ↔ φ ∨ χ ∨ ψ

Proof

Step Hyp Ref Expression
1 orass ⊢ φ ∨ ψ ∨ χ ↔ φ ∨ ψ ∨ χ
2 or12 ⊢ φ ∨ ψ ∨ χ ↔ ψ ∨ φ ∨ χ
3 orcom ⊢ ψ ∨ φ ∨ χ ↔ φ ∨ χ ∨ ψ
4 1 2 3 3bitri ⊢ φ ∨ ψ ∨ χ ↔ φ ∨ χ ∨ ψ