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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3164 |
. 2
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2 | 1 | imp 124 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 |
This theorem is referenced by: elnn 4623 funimass4 5587 fvelimab 5593 ssimaex 5598 funconstss 5655 rexima 5776 ralima 5777 1st2nd 6206 f1o2ndf1 6253 tfri1dALT 6376 eldju1st 7100 axsuploc 8060 lbinf 8935 dfinfre 8943 lbzbi 9646 elfzom1elp1fzo 10232 ssfzo12 10254 seq3split 10510 shftlem 10857 uzwodc 12070 subgintm 13137 subrngintm 13559 subrgintm 13590 tgcl 14021 neipsm 14111 txbasval 14224 elmopn2 14406 metrest 14463 cncfmet 14536 negcncf 14545 reeff1olem 14649 |
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