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Mirrors > Home > MPE Home > Th. List > epel | Structured version Visualization version Unicode version |
Description: The epsilon relation and the membership relation are the same. (Contributed by NM, 13-Aug-1995.) |
Ref | Expression |
---|---|
epel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3203 | . 2 | |
2 | 1 | epelc 5031 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 class class class wbr 4653 cep 5028 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-eprel 5029 |
This theorem is referenced by: epse 5097 dfepfr 5099 epfrc 5100 wecmpep 5106 wetrep 5107 ordon 6982 smoiso 7459 smoiso2 7466 ordunifi 8210 ordiso2 8420 ordtypelem8 8430 wofib 8450 dford2 8517 noinfep 8557 oemapso 8579 wemapwe 8594 alephiso 8921 cflim2 9085 fin23lem27 9150 om2uzisoi 12753 bnj219 30801 efrunt 31590 dftr6 31640 dffr5 31643 elpotr 31686 dfon2lem9 31696 dfon2 31697 domep 31698 brsset 31996 dfon3 31999 brbigcup 32005 brapply 32045 brcup 32046 brcap 32047 dfint3 32059 |
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