Theorem orcomd 377

Description: Commutation of disjuncts in consequent. (Contributed by NM, 2-Dec-2010.)

Hypothesis

Ref	Expression
orcomd.1	⊢ (φ → (ψ ∨ χ))

Assertion

Ref	Expression
orcomd	⊢ (φ → (χ ∨ ψ))

Proof of Theorem orcomd

Step	Hyp	Ref	Expression
1		orcomd.1	. 2 ⊢ (φ → (ψ ∨ χ))
2		orcom 376	. 2 ⊢ ((ψ ∨ χ) ↔ (χ ∨ ψ))
3	1, 2	sylib 188	1 ⊢ (φ → (χ ∨ ψ))

Syntax hints:   → wi 4   ∨ 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:  olcd  382  19.33b  1608  pwadjoin  4119  lefinlteq  4463  vfin1cltv  4547  phi011lem1  4598  erdisj  5972  ncdisjeq  6148  leconnnc  6218