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| Mirrors > Home > ILE Home > Th. List > elab2 | Unicode version | ||
| Description: Membership in a class abstraction, using implicit substitution. (Contributed by NM, 13-Sep-1995.) |
| Ref | Expression |
|---|---|
| elab2.1 |
|
| elab2.2 |
|
| elab2.3 |
|
| Ref | Expression |
|---|---|
| elab2 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elab2.1 |
. 2
| |
| 2 | elab2.2 |
. . 3
| |
| 3 | elab2.3 |
. . 3
| |
| 4 | 2, 3 | elab2g 2919 |
. 2
|
| 5 | 1, 4 | ax-mp 5 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-v 2773 |
| This theorem is referenced by: elpw 3621 elint 3890 opabid 4301 elrn2 4919 elimasn 5048 oprabid 5975 tfrlem3a 6395 tfrcllemsucaccv 6439 tfrcllembxssdm 6441 tfrcllemres 6447 addnqprlemrl 7669 addnqprlemru 7670 addnqprlemfl 7671 addnqprlemfu 7672 mulnqprlemrl 7685 mulnqprlemru 7686 mulnqprlemfl 7687 mulnqprlemfu 7688 ltnqpr 7705 ltnqpri 7706 archpr 7755 cauappcvgprlemladdfu 7766 cauappcvgprlemladdfl 7767 caucvgprlemladdfu 7789 caucvgprprlemopu 7811 suplocexprlemloc 7833 4sqlem12 12667 txuni2 14670 |
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