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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 3151 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wss 3102 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-in 3108 df-ss 3115 |
This theorem is referenced by: sseq12d 3159 eqsstrd 3164 snssg 3692 ssiun2s 3893 treq 4068 onsucsssucexmid 4486 funimass1 5247 feq1 5302 sbcfg 5318 fvmptssdm 5552 fvimacnvi 5581 nnsucsssuc 6439 ereq1 6487 elpm2r 6611 fipwssg 6923 nnnninf 7069 ctssexmid 7093 iscnp 12599 iscnp4 12618 cnntr 12625 cnconst2 12633 cnptopresti 12638 cnptoprest 12639 txbas 12658 txcnp 12671 txdis 12677 txdis1cn 12678 blssps 12827 blss 12828 ssblex 12831 blin2 12832 metss2 12898 metrest 12906 metcnp3 12911 cnopnap 12994 limccl 13028 ellimc3apf 13029 |
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