![]() |
Mathbox for Anthony Hart |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > neufal | 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 |
---|---|
neufal | ⊢ ¬ ∃!𝑥⊥ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nexfal 35791 | . 2 ⊢ ¬ ∃𝑥⊥ | |
2 | euex 2563 | . 2 ⊢ (∃!𝑥⊥ → ∃𝑥⊥) | |
3 | 1, 2 | mto 196 | 1 ⊢ ¬ ∃!𝑥⊥ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ⊥wfal 1545 ∃wex 1773 ∃!weu 2554 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-fal 1546 df-ex 1774 df-eu 2555 |
This theorem is referenced by: unqsym1 35811 |
Copyright terms: Public domain | W3C validator |