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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 3022 |
. 2
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2 | 1 | imp 123 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-in 3008 df-ss 3015 |
This theorem is referenced by: elnn 4435 funimass4 5370 fvelimab 5375 ssimaex 5380 funconstss 5433 rexima 5550 ralima 5551 1st2nd 5967 f1o2ndf1 6009 tfri1dALT 6132 eldju1st 6818 lbinf 8472 dfinfre 8480 lbzbi 9164 elfzom1elp1fzo 9676 ssfzo12 9698 seq3split 9970 iseqsplit 9971 shftlem 10313 tgcl 11827 neipsm 11917 |
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