Theorem or12 509

Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.)

Assertion

Ref	Expression
or12	⊢ ((φ ∨ (ψ ∨ χ)) ↔ (ψ ∨ (φ ∨ χ)))

Proof of Theorem or12

Step	Hyp	Ref	Expression
1		pm1.5 508	. 2 ⊢ ((φ ∨ (ψ ∨ χ)) → (ψ ∨ (φ ∨ χ)))
2		pm1.5 508	. 2 ⊢ ((ψ ∨ (φ ∨ χ)) → (φ ∨ (ψ ∨ χ)))
3	1, 2	impbii 180	1 ⊢ ((φ ∨ (ψ ∨ χ)) ↔ (ψ ∨ (φ ∨ χ)))

This proof depends on syntax axioms:   ↔ wb 176   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  orass  510  or32  513  or4  514  3orcoma  942