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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 384 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
3 | 1, 2 | mpbir 221 | 1 ⊢ (𝜑 ∨ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 |
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 197 df-or 384 |
This theorem is referenced by: orci 404 olci 405 pm2.25 418 exmid 430 pm2.13 433 pm3.12 520 pm5.11 946 pm5.12 947 pm5.14 948 pm5.15 951 pm5.55 957 pm5.54 963 4exmid 1021 rb-ax2 1718 rb-ax3 1719 rb-ax4 1720 exmo 2523 axi12 2629 axbnd 2630 exmidne 2833 ifeqor 4165 fvbr0 6253 letrii 10200 clwwlknondisj 27086 clwwlknondisjOLD 27090 bj-curry 32667 poimirlem26 33565 tsim2 34068 tsbi3 34072 tsan2 34079 tsan3 34080 clsk1indlem2 38657 |
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