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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 3835 | . 2 |
3 | nfsab1 2160 | . . . 4 | |
4 | nfv 1521 | . . . 4 | |
5 | 3, 4 | nfim 1565 | . . 3 |
6 | nfv 1521 | . . 3 | |
7 | eleq1 2233 | . . . . 5 | |
8 | abid 2158 | . . . . 5 | |
9 | 7, 8 | bitrdi 195 | . . . 4 |
10 | eleq2 2234 | . . . 4 | |
11 | 9, 10 | imbi12d 233 | . . 3 |
12 | 5, 6, 11 | cbval 1747 | . 2 |
13 | 2, 12 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1346 wcel 2141 cab 2156 cvv 2730 cint 3829 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-int 3830 |
This theorem is referenced by: elintrab 3841 intmin4 3857 intab 3858 intid 4207 |
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