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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 3061 | . 2 | |
2 | 1 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1465 wss 3041 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 |
This theorem is referenced by: elnn 4489 funimass4 5440 fvelimab 5445 ssimaex 5450 funconstss 5506 rexima 5624 ralima 5625 1st2nd 6047 f1o2ndf1 6093 tfri1dALT 6216 eldju1st 6924 axsuploc 7805 lbinf 8674 dfinfre 8682 lbzbi 9376 elfzom1elp1fzo 9947 ssfzo12 9969 seq3split 10220 shftlem 10556 tgcl 12160 neipsm 12250 txbasval 12363 elmopn2 12545 metrest 12602 cncfmet 12675 negcncf 12684 |
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