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Mirrors > Home > MPE Home > Th. List > ori | Structured version Visualization version GIF version |
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 845 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
3 | 1, 2 | mpbi 229 | 1 ⊢ (¬ 𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 844 |
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 206 df-or 845 |
This theorem is referenced by: 3ori 1423 mtpor 1773 fvrn0 6802 eliman0 6809 onuninsuci 7687 omelon2 7725 infensuc 8942 rankxpsuc 9640 cardlim 9730 alephreg 10338 tskcard 10537 sinhalfpilem 25620 sltres 33865 |
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