Theorem or4 220

Description: Rearrangement of 4 disjuncts.

Assertion

Ref	Expression
or4	⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (ψ ∨ θ)))

Proof of Theorem or4

Step	Hyp	Ref	Expression
1		or12 217	. . 3 ⊢ ((ψ ∨ (χ ∨ θ)) ↔ (χ ∨ (ψ ∨ θ)))
2	1	orbi2i 214	. 2 ⊢ ((φ ∨ (ψ ∨ (χ ∨ θ))) ↔ (φ ∨ (χ ∨ (ψ ∨ θ))))
3		orass 218	. 2 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ (φ ∨ (ψ ∨ (χ ∨ θ))))
4		orass 218	. 2 ⊢ (((φ ∨ χ) ∨ (ψ ∨ θ)) ↔ (φ ∨ (χ ∨ (ψ ∨ θ))))
5	2, 3, 4	3bitr4 158	1 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (ψ ∨ θ)))

Syntax hints:   ↔ wb 127   ∨ wo 195

This theorem is referenced by:  or42 221  orordi 222  orordir 223  ordtri3or 2230

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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