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Mirrors > Home > MPE Home > Th. List > orcoms | Structured version Visualization version GIF version |
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 | pm1.4 868 | . 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 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 210 df-or 847 |
This theorem is referenced by: olcs 875 19.40b 1895 r19.30 3244 propeqop 5364 pwssun 5425 sorpsscmpl 7478 hashinfxadd 13838 swrdnd 14105 pfxnd0 14139 dvasin 35484 dvacos 35485 line2ylem 45631 line2xlem 45633 |
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