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Mirrors > Home > ILE Home > Th. List > sstri | Unicode version |
Description: Subclass transitivity inference. (Contributed by NM, 5-May-2000.) |
Ref | Expression |
---|---|
sstri.1 | |
sstri.2 |
Ref | Expression |
---|---|
sstri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstri.1 | . 2 | |
2 | sstri.2 | . 2 | |
3 | sstr2 3006 | . 2 | |
4 | 1, 2, 3 | mp2 16 | 1 |
Colors of variables: wff set class |
Syntax hints: wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 |
This theorem is referenced by: difdif2ss 3221 difdifdirss 3327 snsstp1 3535 snsstp2 3536 nnregexmid 4360 dmexg 4614 rnexg 4615 ssrnres 4783 cossxp 4863 fabexg 5097 foimacnv 5164 ssimaex 5255 oprabss 5610 tposssxp 5887 dmaddpi 6515 dmmulpi 6516 ltrelxr 7173 nnsscn 8044 nn0sscn 8293 nn0ssq 8713 nnssq 8714 qsscn 8716 fzval2 9032 fzossnn 9198 fzo0ssnn0 9224 serige0 9473 expcl2lemap 9488 rpexpcl 9495 expge0 9512 expge1 9513 infssuzcldc 10347 isprm3 10500 |
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