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| Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994.) | 
| Ref | Expression | 
|---|---|
| ori.1 | ⊢ (𝜑 ∨ 𝜓) | 
| Ref | Expression | 
|---|---|
| ori | ⊢ (¬ 𝜑 → 𝜓) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ori.1 | . 2 ⊢ (𝜑 ∨ 𝜓) | |
| 2 | df-or 848 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
| 3 | 1, 2 | mpbi 230 | 1 ⊢ (¬ 𝜑 → 𝜓) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ¬ wn 3 → 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: 3ori 1425 mtpor 1769 fvrn0 6935 eliman0 6945 onuninsuci 7862 omelon2 7901 infensuc 9196 rankxpsuc 9923 cardlim 10013 alephreg 10623 tskcard 10822 sinhalfpilem 26506 sltres 27708 | 
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