Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > prnzg | Unicode version |
Description: A pair containing a set is not empty. (Contributed by FL, 19-Sep-2011.) |
Ref | Expression |
---|---|
prnzg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3469 | . . 3 | |
2 | 1 | neeq1d 2263 | . 2 |
3 | vex 2604 | . . 3 | |
4 | 3 | prnz 3512 | . 2 |
5 | 2, 4 | vtoclg 2658 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 wne 2245 c0 3251 cpr 3399 |
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-in1 576 ax-in2 577 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-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-v 2603 df-dif 2975 df-un 2977 df-nul 3252 df-sn 3404 df-pr 3405 |
This theorem is referenced by: 0nelop 4003 |
Copyright terms: Public domain | W3C validator |