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Mirrors > Home > ILE Home > Th. List > nfmo1 | GIF version |
Description: Bound-variable hypothesis builder for "at most one". (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfmo1 | ⊢ Ⅎ𝑥∃*𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 2030 | . 2 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑)) | |
2 | nfe1 1496 | . . 3 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
3 | nfeu1 2037 | . . 3 ⊢ Ⅎ𝑥∃!𝑥𝜑 | |
4 | 2, 3 | nfim 1572 | . 2 ⊢ Ⅎ𝑥(∃𝑥𝜑 → ∃!𝑥𝜑) |
5 | 1, 4 | nfxfr 1474 | 1 ⊢ Ⅎ𝑥∃*𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1460 ∃wex 1492 ∃!weu 2026 ∃*wmo 2027 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-eu 2029 df-mo 2030 |
This theorem is referenced by: moanmo 2103 euexex 2111 nfrmo1 2649 mob 2919 morex 2921 funimaexglem 5299 |
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