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Mirrors > Home > ILE Home > Th. List > sseli | Unicode version |
Description: Membership inference from subclass relationship. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sseli.1 |
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Ref | Expression |
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sseli |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseli.1 |
. 2
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2 | ssel 3149 |
. 2
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3 | 1, 2 | ax-mp 5 |
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 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 |
This theorem is referenced by: sselii 3152 sselid 3153 elun1 3302 elun2 3303 finds 4595 finds2 4596 issref 5006 2elresin 5322 fvun1 5577 fvmptssdm 5595 elfvmptrab1 5605 fvimacnvi 5625 elpreima 5630 ofrfval 6084 ofvalg 6085 off 6088 offres 6129 eqopi 6166 op1steq 6173 dfoprab4 6186 f1od2 6229 reldmtpos 6247 smores3 6287 smores2 6288 ctssdccl 7103 pinn 7286 indpi 7319 enq0enq 7408 preqlu 7449 elinp 7451 prop 7452 elnp1st2nd 7453 prarloclem5 7477 cauappcvgprlemladd 7635 peano5nnnn 7869 nnindnn 7870 recn 7922 rexr 7980 peano5nni 8898 nnre 8902 nncn 8903 nnind 8911 nnnn0 9159 nn0re 9161 nn0cn 9162 nn0xnn0 9219 nnz 9248 nn0z 9249 nnq 9609 qcn 9610 rpre 9634 iccshftri 9969 iccshftli 9971 iccdili 9973 icccntri 9975 fzval2 9985 fzelp1 10047 4fvwrd4 10113 elfzo1 10163 expcllem 10504 expcl2lemap 10505 m1expcl2 10515 bcm1k 10711 bcpasc 10717 cau3lem 11094 climconst2 11270 fsum3 11366 binomlem 11462 fprodge1 11618 cos12dec 11746 dvdsflip 11827 infssuzcldc 11922 isprm3 12088 phimullem 12195 prmdiveq 12206 structcnvcnv 12448 fvsetsid 12466 tgval2 13184 qtopbasss 13654 dedekindicc 13744 ivthinc 13754 ivthdec 13755 cosz12 13834 cos0pilt1 13906 ioocosf1o 13908 exmidsbthrlem 14393 |
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