Theorem orordir 517

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

Assertion

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

Proof of Theorem orordir

Step	Hyp	Ref	Expression
1		oridm 500	. . 3 ⊢ ((χ ∨ χ) ↔ χ)
2	1	orbi2i 505	. 2 ⊢ (((φ ∨ ψ) ∨ (χ ∨ χ)) ↔ ((φ ∨ ψ) ∨ χ))
3		or4 514	. 2 ⊢ (((φ ∨ ψ) ∨ (χ ∨ χ)) ↔ ((φ ∨ χ) ∨ (ψ ∨ χ)))
4	2, 3	bitr3i 242	1 ⊢ (((φ ∨ ψ) ∨ χ) ↔ ((φ ∨ χ) ∨ (ψ ∨ χ)))

Syntax hints:   ↔ wb 176   ∨ wo 357

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

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

This theorem is referenced by:  sspsstri  3371