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Mirrors > Home > ILE Home > Th. List > nfeu1 | GIF version |
Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfeu1 | ⊢ Ⅎ𝑥∃!𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 1903 | . 2 ⊢ (∃!𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 ↔ 𝑥 = 𝑦)) | |
2 | nfa1 1434 | . . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 ↔ 𝑥 = 𝑦) | |
3 | 2 | nfex 1528 | . 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 ↔ 𝑥 = 𝑦) |
4 | 1, 3 | nfxfr 1363 | 1 ⊢ Ⅎ𝑥∃!𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 ∀wal 1241 Ⅎwnf 1349 ∃wex 1381 ∃!weu 1900 |
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 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-eu 1903 |
This theorem is referenced by: nfmo1 1912 moaneu 1976 nfreu1 2481 eusv2i 4187 eusv2nf 4188 iota2 4893 sniota 4894 fv3 5197 tz6.12c 5203 eusvobj1 5499 |
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