Theorem orcoms 731

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		pm1.4 728	. 2 ⊢ ((𝜓 ∨ 𝜑) → (𝜑 ∨ 𝜓))
2		orcoms.1	. 2 ⊢ ((𝜑 ∨ 𝜓) → 𝜒)
3	1, 2	syl 14	1 ⊢ ((𝜓 ∨ 𝜑) → 𝜒)

Syntax hints:   → wi 4   ∨ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  olcs  737  dcn  843  xorbin  1395  19.33b2  1643  r19.30dc  2644  pwssunim  4319  omnimkv  7222