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| Mirrors > Home > MPE Home > Th. List > orri | Structured version Visualization version GIF version | ||
| Description: Infer disjunction from implication. (Contributed by NM, 11-Jun-1994.) |
| Ref | Expression |
|---|---|
| orri.1 | ⊢ (¬ 𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| orri | ⊢ (𝜑 ∨ 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | orri.1 | . 2 ⊢ (¬ 𝜑 → 𝜓) | |
| 2 | df-or 849 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
| 3 | 1, 2 | mpbir 231 | 1 ⊢ (𝜑 ∨ 𝜓) |
| Colors of variables: wff setvar class |
| Syntax hints: ¬ wn 3 → wi 4 ∨ wo 848 |
| 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 849 |
| This theorem is referenced by: orci 866 olci 867 pm2.25 890 curryax 894 exmid 895 pm2.13 898 pm5.11g 946 pm5.12 948 pm5.14 949 pm5.55 951 pm3.12 996 pm5.15 1015 pm5.54 1020 4exmid 1052 rb-ax2 1753 rb-ax3 1754 rb-ax4 1755 exmo 2542 axi12 2706 exmidne 2950 ifeqor 4577 fvbr0 6935 letrii 11386 clwwlknondisj 30130 poimirlem26 37653 tsbi3 38142 tsan2 38149 tsan3 38150 clsk1indlem2 44055 |
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