Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > reupick2 | Unicode version |
Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by Mario Carneiro, 15-Dec-2013.) (Proof shortened by Mario Carneiro, 19-Nov-2016.) |
Ref | Expression |
---|---|
reupick2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancr 314 | . . . . . 6 | |
2 | 1 | ralimi 2426 | . . . . 5 |
3 | rexim 2455 | . . . . 5 | |
4 | 2, 3 | syl 14 | . . . 4 |
5 | reupick3 3249 | . . . . . 6 | |
6 | 5 | 3exp 1137 | . . . . 5 |
7 | 6 | com12 30 | . . . 4 |
8 | 4, 7 | syl6 33 | . . 3 |
9 | 8 | 3imp1 1151 | . 2 |
10 | rsp 2411 | . . . 4 | |
11 | 10 | 3ad2ant1 959 | . . 3 |
12 | 11 | imp 122 | . 2 |
13 | 9, 12 | impbid 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wcel 1433 wral 2348 wrex 2349 wreu 2350 |
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 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-ral 2353 df-rex 2354 df-reu 2355 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |