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Mirrors > Home > MPE Home > Th. List > Mathboxes > neutru | 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 |
---|---|
neutru | ⊢ ¬ ∃!𝑥⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nexntru 33752 | . 2 ⊢ ¬ ∃𝑥 ¬ ⊤ | |
2 | eunex 5291 | . 2 ⊢ (∃!𝑥⊤ → ∃𝑥 ¬ ⊤) | |
3 | 1, 2 | mto 199 | 1 ⊢ ¬ ∃!𝑥⊤ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ⊤wtru 1538 ∃wex 1780 ∃!weu 2653 |
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 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-12 2177 ax-nul 5210 ax-pow 5266 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-mo 2622 df-eu 2654 |
This theorem is referenced by: nmotru 33756 |
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