Theorem or23 219

Description: A rearrangement of disjuncts.

Assertion

Ref	Expression
or23	⊢ (((φ ∨ ψ) ∨ χ) ↔ ((φ ∨ χ) ∨ ψ))

Proof of Theorem or23

Step	Hyp	Ref	Expression
1		orcom 209	. . 3 ⊢ ((ψ ∨ χ) ↔ (χ ∨ ψ))
2	1	orbi2i 214	. 2 ⊢ ((φ ∨ (ψ ∨ χ)) ↔ (φ ∨ (χ ∨ ψ)))
3		orass 218	. 2 ⊢ (((φ ∨ ψ) ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))
4		orass 218	. 2 ⊢ (((φ ∨ χ) ∨ ψ) ↔ (φ ∨ (χ ∨ ψ)))
5	2, 3, 4	3bitr4 158	1 ⊢ (((φ ∨ ψ) ∨ χ) ↔ ((φ ∨ χ) ∨ ψ))

Syntax hints:   ↔ wb 127   ∨ wo 195

This theorem is referenced by:  sspsstri 1572  wereu 2197  ordtri3or 2230  ordtri3 2234  psslinpr 3929

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197

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