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Mirrors > Home > MPE Home > Th. List > nfmo1 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for the at-most-one quantifier. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.) Adapt to new definition. (Revised by BJ, 1-Oct-2022.) |
Ref | Expression |
---|---|
nfmo1 | ⊢ Ⅎ𝑥∃*𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 2535 | . 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)) | |
2 | nfa1 2149 | . . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 → 𝑥 = 𝑦) | |
3 | 2 | nfex 2318 | . 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦) |
4 | 1, 3 | nfxfr 1856 | 1 ⊢ Ⅎ𝑥∃*𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 ∃wex 1782 Ⅎwnf 1786 ∃*wmo 2533 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-10 2138 ax-11 2155 ax-12 2172 |
This theorem depends on definitions: df-bi 206 df-or 847 df-ex 1783 df-nf 1787 df-mo 2535 |
This theorem is referenced by: mo3 2559 nfeu1ALT 2584 moanmo 2619 moexexlem 2623 mopick2 2634 2mo 2645 2eu3 2650 nfrmo1 3408 mob 3714 morex 3716 wl-mo3t 36441 |
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