Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > euabsn | Unicode version |
Description: Another way to express existential uniqueness of a wff: its class abstraction is a singleton. (Contributed by NM, 22-Feb-2004.) |
Ref | Expression |
---|---|
euabsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euabsn2 3650 | . 2 | |
2 | nfv 1521 | . . 3 | |
3 | nfab1 2314 | . . . 4 | |
4 | 3 | nfeq1 2322 | . . 3 |
5 | sneq 3592 | . . . 4 | |
6 | 5 | eqeq2d 2182 | . . 3 |
7 | 2, 4, 6 | cbvex 1749 | . 2 |
8 | 1, 7 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1348 wex 1485 weu 2019 cab 2156 csn 3581 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sn 3587 |
This theorem is referenced by: eusn 3655 args 4978 mapsn 6666 |
Copyright terms: Public domain | W3C validator |