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Mirrors > Home > ILE Home > Th. List > sstrdi | Unicode version |
Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
sstrdi.1 | |
sstrdi.2 |
Ref | Expression |
---|---|
sstrdi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstrdi.1 | . 2 | |
2 | sstrdi.2 | . . 3 | |
3 | 2 | a1i 9 | . 2 |
4 | 1, 3 | sstrd 3107 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wss 3071 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-in 3077 df-ss 3084 |
This theorem is referenced by: difss2 3204 sstpr 3684 rintm 3905 eqbrrdva 4709 dmxpss2 4971 rnxpss2 4972 ssxpbm 4974 ssxp1 4975 ssxp2 4976 relfld 5067 funssxp 5292 dff2 5564 fliftf 5700 1stcof 6061 2ndcof 6062 tfrlemibfn 6225 tfr1onlembfn 6241 tfrcllemssrecs 6249 tfrcllembfn 6254 sucinc2 6342 peano5nnnn 7700 peano5nni 8723 suprzclex 9149 ioodisj 9776 fzssnn 9848 fzossnn0 9952 elfzom1elp1fzo 9979 frecuzrdgtcl 10185 frecuzrdgdomlem 10190 frecuzrdgfunlem 10192 zfz1iso 10584 seq3coll 10585 summodclem2a 11150 summodclem2 11151 zsumdc 11153 fsumsersdc 11164 fsum3cvg3 11165 prodmodclem2a 11345 prodmodclem2 11346 exmidunben 11939 strsetsid 11992 lmss 12415 dvbssntrcntop 12822 dvcjbr 12841 peano5set 13138 |
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