Theorem or32 513

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

Assertion

Ref	Expression
or32	⊢ (((φ ∨ ψ) ∨ χ) ↔ ((φ ∨ χ) ∨ ψ))

Proof of Theorem or32

Step	Hyp	Ref	Expression
1		orass 510	. 2 ⊢ (((φ ∨ ψ) ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))
2		or12 509	. 2 ⊢ ((φ ∨ (ψ ∨ χ)) ↔ (ψ ∨ (φ ∨ χ)))
3		orcom 376	. 2 ⊢ ((ψ ∨ (φ ∨ χ)) ↔ ((φ ∨ χ) ∨ ψ))
4	1, 2, 3	3bitri 262	1 ⊢ (((φ ∨ ψ) ∨ χ) ↔ ((φ ∨ χ) ∨ ψ))

This proof depends on syntax axioms:   ↔ wb 176   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  sspsstri  3372  sfin111  4537