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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 3115 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wss 3066 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-in 3072 df-ss 3079 |
This theorem is referenced by: sseq12d 3123 eqsstrd 3128 snssg 3651 ssiun2s 3852 treq 4027 onsucsssucexmid 4437 funimass1 5195 feq1 5250 sbcfg 5266 fvmptssdm 5498 fvimacnvi 5527 nnsucsssuc 6381 ereq1 6429 elpm2r 6553 fipwssg 6860 nnnninf 7016 ctssexmid 7017 iscnp 12357 iscnp4 12376 cnntr 12383 cnconst2 12391 cnptopresti 12396 cnptoprest 12397 txbas 12416 txcnp 12429 txdis 12435 txdis1cn 12436 blssps 12585 blss 12586 ssblex 12589 blin2 12590 metss2 12656 metrest 12664 metcnp3 12669 cnopnap 12752 limccl 12786 ellimc3apf 12787 |
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