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Mirrors > Home > ILE Home > Th. List > ssel | Unicode version |
Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
ssel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 2928 |
. . . . . 6
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2 | 1 | biimpi 113 |
. . . . 5
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3 | 2 | 19.21bi 1447 |
. . . 4
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4 | 3 | anim2d 320 |
. . 3
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5 | 4 | eximdv 1757 |
. 2
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6 | df-clel 2033 |
. 2
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7 | df-clel 2033 |
. 2
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8 | 5, 6, 7 | 3imtr4g 194 |
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 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-in 2918 df-ss 2925 |
This theorem is referenced by: ssel2 2934 sseli 2935 sseld 2938 sstr2 2946 ssralv 2998 ssrexv 2999 ralss 3000 rexss 3001 ssconb 3070 sscon 3071 ssdif 3072 unss1 3106 ssrin 3156 difin2 3193 reuss2 3211 reupick 3215 sssnm 3516 uniss 3592 ss2iun 3663 ssiun 3690 iinss 3699 disjss2 3739 disjss1 3742 pwnss 3903 sspwb 3943 ssopab2b 4004 soss 4042 sucssel 4127 ssorduni 4179 onnmin 4244 ssnel 4245 ssrel 4371 ssrel2 4373 ssrelrel 4383 xpss12 4388 cnvss 4451 dmss 4477 elreldm 4503 dmcosseq 4546 relssres 4591 iss 4597 resopab2 4598 issref 4650 ssrnres 4706 dfco2a 4764 cores 4767 funssres 4885 fununi 4910 funimaexglem 4925 dfimafn 5165 funimass4 5167 funimass3 5226 dff4im 5256 funfvima2 5334 funfvima3 5335 f1elima 5355 riotass2 5437 ssoprab2b 5504 resoprab2 5540 releldm2 5753 reldmtpos 5809 dmtpos 5812 rdgss 5910 eqreznegel 8325 negm 8326 iccsupr 8605 bdop 9330 bj-nnen2lp 9414 |
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