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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 2540 | . 2 ⊢ (∃*𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦)) | |
| 2 | nfa1 2151 | . . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 → 𝑥 = 𝑦) | |
| 3 | 2 | nfex 2324 | . 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 → 𝑥 = 𝑦) |
| 4 | 1, 3 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥∃*𝑥𝜑 |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∀wal 1538 ∃wex 1779 Ⅎwnf 1783 ∃*wmo 2538 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-11 2157 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-or 849 df-ex 1780 df-nf 1784 df-mo 2540 |
| This theorem is referenced by: mo3 2564 nfeu1ALT 2589 moanmo 2622 moexexlem 2626 mopick2 2637 2mo 2648 2eu3 2654 nfrmo1 3411 mob 3723 morex 3725 wl-mo3t 37577 |
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