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Mirrors > Home > ILE Home > Th. List > prmg | Unicode version |
Description: A pair containing a set is inhabited. (Contributed by Jim Kingdon, 21-Sep-2018.) |
Ref | Expression |
---|---|
prmg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snmg 3688 | . 2 | |
2 | orc 702 | . . . 4 | |
3 | velsn 3587 | . . . 4 | |
4 | vex 2724 | . . . . 5 | |
5 | 4 | elpr 3591 | . . . 4 |
6 | 2, 3, 5 | 3imtr4i 200 | . . 3 |
7 | 6 | eximi 1587 | . 2 |
8 | 1, 7 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 698 wceq 1342 wex 1479 wcel 2135 csn 3570 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-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-v 2723 df-un 3115 df-sn 3576 df-pr 3577 |
This theorem is referenced by: prm 3693 opm 4206 onintexmid 4544 |
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