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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 711 | . 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜓 ∨ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ∨ wo 708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-io 709 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: falortru 1407 sucidg 4416 finexdc 6901 finomni 7137 indpi 7340 1ap0 8545 iap0 9140 pnf0xnn0 9244 bcn1 10733 sum0 11391 prod0 11588 odd2np1lem 11871 lcm0val 12059 ex-or 14394 dcapnconst 14728 |
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