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Mirrors > Home > MPE Home > Th. List > Mathboxes > unnf | 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 |
---|---|
unnf | ⊢ ¬ ∃!𝑥⊥ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nextf 31575 | . 2 ⊢ ¬ ∃𝑥⊥ | |
2 | euex 2482 | . 2 ⊢ (∃!𝑥⊥ → ∃𝑥⊥) | |
3 | 1, 2 | mto 187 | 1 ⊢ ¬ ∃!𝑥⊥ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ⊥wfal 1480 ∃wex 1695 ∃!weu 2458 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 |
This theorem depends on definitions: df-bi 196 df-tru 1478 df-fal 1481 df-ex 1696 df-eu 2462 |
This theorem is referenced by: unqsym1 31594 |
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