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Mirrors > Home > MPE Home > Th. List > Mathboxes > unnt | Structured version Visualization version GIF version |
Description: There does not exist exactly one set, such that ⊤ is true. (Contributed by Anthony Hart, 13-Sep-2011.) |
Ref | Expression |
---|---|
unnt | ⊢ ¬ ∃!𝑥⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nextnt 32404 | . 2 ⊢ ¬ ∃𝑥 ¬ ⊤ | |
2 | eunex 4859 | . 2 ⊢ (∃!𝑥⊤ → ∃𝑥 ¬ ⊤) | |
3 | 1, 2 | mto 188 | 1 ⊢ ¬ ∃!𝑥⊤ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ⊤wtru 1484 ∃wex 1704 ∃!weu 2470 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-nul 4789 ax-pow 4843 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 |
This theorem is referenced by: mont 32408 |
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