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| Mirrors > Home > MPE Home > Th. List > nfeuw | Structured version Visualization version GIF version | ||
| Description: Bound-variable hypothesis builder for the unique existential quantifier. Version of nfeu 2593 with a disjoint variable condition, which does not require ax-13 2376. (Contributed by NM, 8-Mar-1995.) Avoid ax-13 2376. (Revised by GG, 10-Jan-2024.) | 
| Ref | Expression | 
|---|---|
| nfeuw.1 | ⊢ Ⅎ𝑥𝜑 | 
| Ref | Expression | 
|---|---|
| nfeuw | ⊢ Ⅎ𝑥∃!𝑦𝜑 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | nftru 1803 | . . 3 ⊢ Ⅎ𝑦⊤ | |
| 2 | nfeuw.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
| 3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) | 
| 4 | 1, 3 | nfeudw 2590 | . 2 ⊢ (⊤ → Ⅎ𝑥∃!𝑦𝜑) | 
| 5 | 4 | mptru 1546 | 1 ⊢ Ⅎ𝑥∃!𝑦𝜑 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ⊤wtru 1540 Ⅎwnf 1782 ∃!weu 2567 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-10 2140 ax-11 2156 ax-12 2176 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1542 df-ex 1779 df-nf 1783 df-mo 2539 df-eu 2568 | 
| This theorem is referenced by: nfreuw 3413 eusv2nf 5394 reusv2lem3 5399 bnj1489 35071 setrec2 49269 | 
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