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Mirrors > Home > NFE Home > Th. List > sseld | Unicode version |
Description: Membership deduction from subclass relationship. (Contributed by NM, 15-Nov-1995.) |
Ref | Expression |
---|---|
sseld.1 |
Ref | Expression |
---|---|
sseld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseld.1 | . 2 | |
2 | ssel 3267 | . 2 | |
3 | 1, 2 | syl 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1710 wss 3257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 |
This theorem is referenced by: sselda 3273 sseldd 3274 ssneld 3275 elelpwi 3732 findsd 4410 sfinltfin 4535 ssbrd 4680 opelf 5235 fun11iun 5305 fvimacnv 5403 ffvelrn 5415 dff3 5420 dff4 5421 enprmaplem3 6078 spacind 6287 dmfrec 6316 |
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