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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 848 | . 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 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: orci 865 olci 866 pm2.25 889 curryax 893 exmid 894 pm2.13 897 pm5.11g 945 pm5.12 947 pm5.14 948 pm5.55 950 pm3.12 995 pm5.15 1014 pm5.54 1019 4exmid 1051 rb-ax2 1749 rb-ax3 1750 rb-ax4 1751 exmo 2539 axi12 2703 exmidne 2947 ifeqor 4581 fvbr0 6935 letrii 11383 clwwlknondisj 30139 poimirlem26 37632 tsbi3 38121 tsan2 38128 tsan3 38129 clsk1indlem2 44031 |
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