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| Mirrors > Home > ILE Home > Th. List > elintab | Unicode version | ||
| Description: Membership in the intersection of a class abstraction. (Contributed by NM, 30-Aug-1993.) |
| Ref | Expression |
|---|---|
| inteqab.1 |
|
| Ref | Expression |
|---|---|
| elintab |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | inteqab.1 |
. . 3
| |
| 2 | 1 | elint 3891 |
. 2
|
| 3 | nfsab1 2195 |
. . . 4
| |
| 4 | nfv 1551 |
. . . 4
| |
| 5 | 3, 4 | nfim 1595 |
. . 3
|
| 6 | nfv 1551 |
. . 3
| |
| 7 | eleq1 2268 |
. . . . 5
| |
| 8 | abid 2193 |
. . . . 5
| |
| 9 | 7, 8 | bitrdi 196 |
. . . 4
|
| 10 | eleq2 2269 |
. . . 4
| |
| 11 | 9, 10 | imbi12d 234 |
. . 3
|
| 12 | 5, 6, 11 | cbval 1777 |
. 2
|
| 13 | 2, 12 | bitri 184 |
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 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-ext 2187 |
| This theorem depends on definitions: df-bi 117 df-tru 1376 df-nf 1484 df-sb 1786 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-v 2774 df-int 3886 |
| This theorem is referenced by: elintrab 3897 intmin4 3913 intab 3914 intid 4268 |
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