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Mathbox for Anthony Hart |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > mofal | Structured version Visualization version GIF version |
Description: There exist at most one set such that ⊥ is true. (Contributed by Anthony Hart, 13-Sep-2011.) |
Ref | Expression |
---|---|
mofal | ⊢ ∃*𝑥⊥ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nexfal 32988 | . 2 ⊢ ¬ ∃𝑥⊥ | |
2 | exmo 2554 | . 2 ⊢ (∃𝑥⊥ ∨ ∃*𝑥⊥) | |
3 | 1, 2 | mtpor 1814 | 1 ⊢ ∃*𝑥⊥ |
Colors of variables: wff setvar class |
Syntax hints: ⊥wfal 1614 ∃wex 1823 ∃*wmo 2549 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 |
This theorem depends on definitions: df-bi 199 df-or 837 df-tru 1605 df-fal 1615 df-ex 1824 df-mo 2551 |
This theorem is referenced by: amosym1 33008 |
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