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Mirrors > Home > ILE Home > Th. List > sseq1d | Unicode version |
Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
sseq1d.1 |
Ref | Expression |
---|---|
sseq1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1d.1 | . 2 | |
2 | sseq1 3170 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 wss 3121 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-in 3127 df-ss 3134 |
This theorem is referenced by: sseq12d 3178 eqsstrd 3183 snssg 3716 ssiun2s 3917 treq 4093 onsucsssucexmid 4511 funimass1 5275 feq1 5330 sbcfg 5346 fvmptssdm 5580 fvimacnvi 5610 nnsucsssuc 6471 ereq1 6520 elpm2r 6644 fipwssg 6956 nnnninf 7102 ctssexmid 7126 iscnp 12993 iscnp4 13012 cnntr 13019 cnconst2 13027 cnptopresti 13032 cnptoprest 13033 txbas 13052 txcnp 13065 txdis 13071 txdis1cn 13072 blssps 13221 blss 13222 ssblex 13225 blin2 13226 metss2 13292 metrest 13300 metcnp3 13305 cnopnap 13388 limccl 13422 ellimc3apf 13423 |
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