Theorem orordi 222

Description: Distribution of disjunction over disjunction.

Assertion

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

Proof of Theorem orordi

Step	Hyp	Ref	Expression
1		oridm 208	. . 3 ⊢ ((φ ∨ φ) ↔ φ)
2	1	orbi1i 215	. 2 ⊢ (((φ ∨ φ) ∨ (ψ ∨ χ)) ↔ (φ ∨ (ψ ∨ χ)))
3		or4 220	. 2 ⊢ (((φ ∨ φ) ∨ (ψ ∨ χ)) ↔ ((φ ∨ ψ) ∨ (φ ∨ χ)))
4	2, 3	bitr3 153	1 ⊢ ((φ ∨ (ψ ∨ χ)) ↔ ((φ ∨ ψ) ∨ (φ ∨ χ)))

Syntax hints:   ↔ wb 127   ∨ wo 195

This theorem is referenced by:  pm2.85 439

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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