Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eueq | Unicode version |
Description: Equality has existential uniqueness. (Contributed by NM, 25-Nov-1994.) |
Ref | Expression |
---|---|
eueq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr3 2100 | . . . 4 | |
2 | 1 | gen2 1379 | . . 3 |
3 | 2 | biantru 296 | . 2 |
4 | isset 2605 | . 2 | |
5 | eqeq1 2087 | . . 3 | |
6 | 5 | eu4 2003 | . 2 |
7 | 3, 4, 6 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 weu 1941 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: eueq1 2764 moeq 2767 mosubt 2769 reuhypd 4221 mptfng 5044 |
Copyright terms: Public domain | W3C validator |