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| Mirrors > Home > MPE Home > Th. List > exmo | Structured version Visualization version GIF version | ||
| Description: Any proposition holds for some 𝑥 or holds for at most one 𝑥. (Contributed by NM, 8-Mar-1995.) Shorten proof and avoid df-eu 2568. (Revised by BJ, 14-Oct-2022.) | 
| Ref | Expression | 
|---|---|
| exmo | ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | nexmo 2540 | . 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑) | |
| 2 | 1 | orri 862 | 1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∨ wo 847 ∃wex 1778 ∃*wmo 2537 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 | 
| This theorem depends on definitions: df-bi 207 df-or 848 df-ex 1779 df-mo 2539 | 
| This theorem is referenced by: brdom3 10569 mofal 36411 | 
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