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Mirrors > Home > ILE Home > Th. List > olci | GIF version |
Description: Deduction introducing a disjunct. (Contributed by NM, 19-Jan-2008.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
orci.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
olci | ⊢ (𝜓 ∨ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orci.1 | . 2 ⊢ 𝜑 | |
2 | olc 665 | . 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝜓 ∨ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ∨ wo 662 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-io 663 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: falortru 1341 sucidg 4210 finexdc 6548 finomni 6717 indpi 6822 1ap0 7985 iap0 8549 pnf0xnn0 8653 bcn1 10015 odd2np1lem 10666 lcm0val 10841 ex-or 11007 |
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