![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 | pm1.4 869 | . 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 1886 r19.30OLD 3119 propeqop 5517 pwssun 5580 sorpsscmpl 7753 hashinfxadd 14421 swrdnd 14689 pfxnd0 14723 dvasin 37691 dvacos 37692 line2ylem 48601 line2xlem 48603 |
Copyright terms: Public domain | W3C validator |