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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 846 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
3 | 1, 2 | mpbir 230 | 1 ⊢ (𝜑 ∨ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 845 |
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 846 |
This theorem is referenced by: orci 863 olci 864 pm2.25 888 curryax 892 exmid 893 pm2.13 896 pm5.11g 942 pm5.12 944 pm5.14 945 pm5.55 947 pm3.12 992 pm5.15 1011 pm5.54 1016 4exmid 1050 rb-ax2 1755 rb-ax3 1756 rb-ax4 1757 exmo 2535 axi12 2700 exmidne 2949 ifeqor 4573 fvbr0 6907 letrii 11321 clwwlknondisj 29229 poimirlem26 36318 tsbi3 36808 tsan2 36815 tsan3 36816 clsk1indlem2 42564 |
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