Theorem orcoms 871

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		pm1.4 868	. 2 ⊢ ((𝜓 ∨ 𝜑) → (𝜑 ∨ 𝜓))
2		orcoms.1	. 2 ⊢ ((𝜑 ∨ 𝜓) → 𝜒)
3	1, 2	syl 17	1 ⊢ ((𝜓 ∨ 𝜑) → 𝜒)

Syntax hints:   → wi 4   ∨ wo 846

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 206  df-or 847

This theorem is referenced by:  olcs  875  19.40b  1884  r19.30OLD  3116  propeqop  5503  pwssun  5567  sorpsscmpl  7733  hashinfxadd  14368  swrdnd  14628  pfxnd0  14662  dvasin  37112  dvacos  37113  line2ylem  47747  line2xlem  47749