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Mirrors > Home > MPE Home > Th. List > exmo | Structured version Visualization version GIF version |
Description: Something exists or at most one exists. (Contributed by NM, 8-Mar-1995.) |
Ref | Expression |
---|---|
exmo | ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.21 119 | . . 3 ⊢ (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∃!𝑥𝜑)) | |
2 | df-mo 2463 | . . 3 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑)) | |
3 | 1, 2 | sylibr 223 | . 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑) |
4 | 3 | orri 390 | 1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 ∃wex 1695 ∃!weu 2458 ∃*wmo 2459 |
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 196 df-or 384 df-mo 2463 |
This theorem is referenced by: exmoeu 2490 moanim 2517 moexex 2529 mo2icl 3352 mosubopt 4897 dff3 6280 brdom3 9231 mof 31579 |
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