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Mirrors > Home > MPE Home > Th. List > Mathboxes > nextnt | Structured version Visualization version GIF version |
Description: There does not exist a set, such that ⊤ is not true. (Contributed by Anthony Hart, 13-Sep-2011.) |
Ref | Expression |
---|---|
nextnt | ⊢ ¬ ∃𝑥 ¬ ⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1487 | . . 3 ⊢ ⊤ | |
2 | 1 | notnoti 137 | . 2 ⊢ ¬ ¬ ⊤ |
3 | 2 | nex 1731 | 1 ⊢ ¬ ∃𝑥 ¬ ⊤ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ⊤wtru 1484 ∃wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 |
This theorem depends on definitions: df-bi 197 df-tru 1486 df-ex 1705 |
This theorem is referenced by: unnt 32407 |
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