Theorem or42 515

Description: Rearrangement of 4 disjuncts. (Contributed by NM, 10-Jan-2005.)

Assertion

Ref	Expression
or42	⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (θ ∨ ψ)))

Proof of Theorem or42

Step	Hyp	Ref	Expression
1		or4 514	. 2 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (ψ ∨ θ)))
2		orcom 376	. . 3 ⊢ ((ψ ∨ θ) ↔ (θ ∨ ψ))
3	2	orbi2i 505	. 2 ⊢ (((φ ∨ χ) ∨ (ψ ∨ θ)) ↔ ((φ ∨ χ) ∨ (θ ∨ ψ)))
4	1, 3	bitri 240	1 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (θ ∨ ψ)))

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: (None)