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Mirrors > Home > ILE Home > Th. List > sstrd | Unicode version |
Description: Subclass transitivity deduction. (Contributed by NM, 2-Jun-2004.) |
Ref | Expression |
---|---|
sstrd.1 |
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sstrd.2 |
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Ref | Expression |
---|---|
sstrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstrd.1 |
. 2
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2 | sstrd.2 |
. 2
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3 | sstr 3178 |
. 2
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4 | 1, 2, 3 | syl2anc 411 |
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: sstrid 3181 sstrdi 3182 ssdif2d 3289 tfisi 4601 funss 5250 fssxp 5398 fvmptssdm 5616 suppssfv 6097 suppssov1 6098 tposss 6265 tfrlem1 6327 tfrlemibfn 6347 tfr1onlembfn 6363 tfr1onlemubacc 6365 tfr1onlemres 6368 tfrcllembfn 6376 tfrcllemubacc 6378 tfrcllemres 6381 ecinxp 6628 undifdc 6941 sbthlem1 6974 iseqf1olemnab 10506 fiubm 10826 isumss 11417 prodssdc 11615 ennnfoneleminc 12430 strsetsid 12513 strleund 12581 strext 12583 imasaddvallemg 12758 subsubm 12901 subsubg 13102 subgintm 13103 subsubrng 13522 subsubrg 13553 lssintclm 13661 lspss 13676 lspun 13679 lsslsp 13706 ntrss 14016 neiint 14042 neiss 14047 restopnb 14078 iscnp4 14115 blssps 14324 blss 14325 xmettx 14407 tgqioo 14444 rescncf 14465 suplociccreex 14499 suplociccex 14500 dvbss 14551 dvbsssg 14552 dvfgg 14554 dvcnp2cntop 14560 dvcn 14561 dvaddxxbr 14562 dvmulxxbr 14563 dvcoapbr 14568 |
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