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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 2022 | . 2 ⊢ (∃!𝑥𝜑 ↔ ∃𝑦∀𝑥(𝜑 ↔ 𝑥 = 𝑦)) | |
2 | nfa1 1534 | . . 3 ⊢ Ⅎ𝑥∀𝑥(𝜑 ↔ 𝑥 = 𝑦) | |
3 | 2 | nfex 1630 | . 2 ⊢ Ⅎ𝑥∃𝑦∀𝑥(𝜑 ↔ 𝑥 = 𝑦) |
4 | 1, 3 | nfxfr 1467 | 1 ⊢ Ⅎ𝑥∃!𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∀wal 1346 Ⅎwnf 1453 ∃wex 1485 ∃!weu 2019 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-eu 2022 |
This theorem is referenced by: nfmo1 2031 moaneu 2095 nfreu1 2641 eusv2i 4440 eusv2nf 4441 iota2 5188 sniota 5189 fv3 5519 tz6.12c 5526 eusvobj1 5840 |
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