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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 3647 | . . 3 | |
2 | 1 | neeq1d 2352 | . 2 |
3 | vex 2724 | . . 3 | |
4 | 3 | prnz 3692 | . 2 |
5 | 2, 4 | vtoclg 2781 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 wne 2334 c0 3404 cpr 3571 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-v 2723 df-dif 3113 df-un 3115 df-nul 3405 df-sn 3576 df-pr 3577 |
This theorem is referenced by: 0nelop 4220 |
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