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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 2654. (Revised by BJ, 14-Oct-2022.) |
Ref | Expression |
---|---|
exmo | ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nexmo 2623 | . 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑) | |
2 | 1 | orri 858 | 1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∨ wo 843 ∃wex 1780 ∃*wmo 2620 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 |
This theorem depends on definitions: df-bi 209 df-or 844 df-ex 1781 df-mo 2622 |
This theorem is referenced by: brdom3 9950 mofal 33757 |
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