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Mirrors > Home > ILE Home > Th. List > ssel2 | Unicode version |
Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004.) |
Ref | Expression |
---|---|
ssel2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3122 | . 2 | |
2 | 1 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2128 wss 3102 |
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-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-ss 3115 |
This theorem is referenced by: elnn 4567 funimass4 5521 fvelimab 5526 ssimaex 5531 funconstss 5587 rexima 5707 ralima 5708 1st2nd 6131 f1o2ndf1 6177 tfri1dALT 6300 eldju1st 7017 axsuploc 7952 lbinf 8824 dfinfre 8832 lbzbi 9531 elfzom1elp1fzo 10110 ssfzo12 10132 seq3split 10387 shftlem 10727 tgcl 12534 neipsm 12624 txbasval 12737 elmopn2 12919 metrest 12976 cncfmet 13049 negcncf 13058 reeff1olem 13162 |
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