Theorem orordi 516

Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.)

Assertion

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

Proof of Theorem orordi

Step	Hyp	Ref	Expression
1		oridm 500	. . 3 ⊢ ((φ ∨ φ) ↔ φ)
2	1	orbi1i 506	. 2 ⊢ (((φ ∨ φ) ∨ (ψ ∨ χ)) ↔ (φ ∨ (ψ ∨ χ)))
3		or4 514	. 2 ⊢ (((φ ∨ φ) ∨ (ψ ∨ χ)) ↔ ((φ ∨ ψ) ∨ (φ ∨ χ)))
4	2, 3	bitr3i 242	1 ⊢ ((φ ∨ (ψ ∨ χ)) ↔ ((φ ∨ ψ) ∨ (φ ∨ χ)))

Syntax hints:   ↔ wb 176   ∨ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by:  pm4.78  565