Theorem orass 218

Description: Associative law for disjunction. Theorem *4.33 of [WhiteheadRussell] p. 118.

Assertion

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

Proof of Theorem orass

Step	Hyp	Ref	Expression
1		or12 217	. 2 ⊢ ((χ ∨ (φ ∨ ψ)) ↔ (φ ∨ (χ ∨ ψ)))
2		orcom 209	. 2 ⊢ (((φ ∨ ψ) ∨ χ) ↔ (χ ∨ (φ ∨ ψ)))
3		orcom 209	. . 3 ⊢ ((ψ ∨ χ) ↔ (χ ∨ ψ))
4	3	orbi2i 214	. 2 ⊢ ((φ ∨ (ψ ∨ χ)) ↔ (φ ∨ (χ ∨ ψ)))
5	1, 2, 4	3bitr4 158	1 ⊢ (((φ ∨ ψ) ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))

Syntax hints:   ↔ wb 127   ∨ wo 195

This theorem is referenced by:  or23 219  or4 220  3orass 584  eueq3 1430  unass 1615

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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