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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 1901 | . 2 ⊢ (∃*xφ ↔ (∃xφ → ∃!xφ)) | |
2 | nfe1 1382 | . . 3 ⊢ Ⅎx∃xφ | |
3 | nfeu1 1908 | . . 3 ⊢ Ⅎx∃!xφ | |
4 | 2, 3 | nfim 1461 | . 2 ⊢ Ⅎx(∃xφ → ∃!xφ) |
5 | 1, 4 | nfxfr 1360 | 1 ⊢ Ⅎx∃*xφ |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1346 ∃wex 1378 ∃!weu 1897 ∃*wmo 1898 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-eu 1900 df-mo 1901 |
This theorem is referenced by: moanmo 1974 euexex 1982 nfrmo1 2476 mob 2717 morex 2719 funimaexglem 4925 |
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