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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 845 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
3 | 1, 2 | mpbir 234 | 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 210 df-or 845 |
This theorem is referenced by: orci 862 olci 863 pm2.25 887 curryax 891 exmid 892 pm2.13 895 pm5.11g 941 pm5.12 943 pm5.14 944 pm5.55 946 pm3.12 991 pm5.15 1010 pm5.54 1015 4exmid 1047 rb-ax2 1755 rb-ax3 1756 rb-ax4 1757 exmo 2600 axi12 2768 exmidne 2997 ifeqor 4474 fvbr0 6672 letrii 10754 clwwlknondisj 27896 poimirlem26 35083 tsbi3 35573 tsan2 35580 tsan3 35581 clsk1indlem2 40745 |
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