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| Description: Commutation of disjuncts in antecedent. (Contributed by NM, 2-Dec-2012.) | 
| Ref | Expression | 
|---|---|
| orcoms.1 | ⊢ ((𝜑 ∨ 𝜓) → 𝜒) | 
| Ref | Expression | 
|---|---|
| orcoms | ⊢ ((𝜓 ∨ 𝜑) → 𝜒) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | pm1.4 869 | . 2 ⊢ ((𝜓 ∨ 𝜑) → (𝜑 ∨ 𝜓)) | |
| 2 | orcoms.1 | . 2 ⊢ ((𝜑 ∨ 𝜓) → 𝜒) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ ((𝜓 ∨ 𝜑) → 𝜒) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∨ wo 847 | 
| 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 207 df-or 848 | 
| This theorem is referenced by: olcs 876 19.40b 1887 r19.30OLD 3120 propeqop 5511 pwssun 5574 sorpsscmpl 7755 hashinfxadd 14425 swrdnd 14693 pfxnd0 14727 dvasin 37712 dvacos 37713 line2ylem 48677 line2xlem 48679 | 
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