Theorem orcoms 378

Description: Commutation of disjuncts in antecedent. (Contributed by NM, 2-Dec-2012.)

Hypothesis

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

Assertion

Ref	Expression
orcoms	⊢ ((ψ ∨ φ) → χ)

Proof of Theorem orcoms

Step	Hyp	Ref	Expression
1		pm1.4 375	. 2 ⊢ ((ψ ∨ φ) → (φ ∨ ψ))
2		orcoms.1	. 2 ⊢ ((φ ∨ ψ) → χ)
3	1, 2	syl 15	1 ⊢ ((ψ ∨ φ) → χ)

Syntax hints:   → wi 4   ∨ 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:  olcs  384