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Mirrors > Home > MPE Home > Th. List > Mathboxes > mont | Structured version Visualization version GIF version |
Description: There does not exist at most one set, such that ⊤ is true. (Contributed by Anthony Hart, 13-Sep-2011.) |
Ref | Expression |
---|---|
mont | ⊢ ¬ ∃*𝑥⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | extt 31573 | . . 3 ⊢ ∃𝑥⊤ | |
2 | unnt 31577 | . . 3 ⊢ ¬ ∃!𝑥⊤ | |
3 | mth8 157 | . . 3 ⊢ (∃𝑥⊤ → (¬ ∃!𝑥⊤ → ¬ (∃𝑥⊤ → ∃!𝑥⊤))) | |
4 | 1, 2, 3 | mp2 9 | . 2 ⊢ ¬ (∃𝑥⊤ → ∃!𝑥⊤) |
5 | df-mo 2463 | . 2 ⊢ (∃*𝑥⊤ ↔ (∃𝑥⊤ → ∃!𝑥⊤)) | |
6 | 4, 5 | mtbir 312 | 1 ⊢ ¬ ∃*𝑥⊤ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ⊤wtru 1476 ∃wex 1695 ∃!weu 2458 ∃*wmo 2459 |
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 ax-7 1922 ax-8 1979 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-nul 4717 ax-pow 4769 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-eu 2462 df-mo 2463 |
This theorem is referenced by: (None) |
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