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| Mirrors > Home > MPE Home > Th. List > nfmov | Structured version Visualization version GIF version | ||
| Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2562 for a version without disjoint variable conditions but requiring ax-13 2377. (Contributed by NM, 9-Mar-1995.) (Revised by Wolf Lammen, 2-Oct-2023.) |
| Ref | Expression |
|---|---|
| nfmov.1 | ⊢ Ⅎ𝑥𝜑 |
| Ref | Expression |
|---|---|
| nfmov | ⊢ Ⅎ𝑥∃*𝑦𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nftru 1804 | . . 3 ⊢ Ⅎ𝑦⊤ | |
| 2 | nfmov.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
| 3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
| 4 | 1, 3 | nfmodv 2559 | . 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑) |
| 5 | 4 | mptru 1547 | 1 ⊢ Ⅎ𝑥∃*𝑦𝜑 |
| Colors of variables: wff setvar class |
| Syntax hints: ⊤wtru 1541 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-tru 1543 df-ex 1780 df-nf 1784 df-mo 2540 |
| This theorem is referenced by: mo3 2564 2moexv 2627 moexexvw 2628 2moswapv 2629 2euexv 2631 2mo 2648 nfrmow 3413 reusv1 5397 reusv2lem1 5398 mosubopt 5515 dffun6f 6579 |
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