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Mirrors > Home > ILE Home > Th. List > iinab | Unicode version |
Description: Indexed intersection of a class builder. (Contributed by NM, 6-Dec-2011.) |
Ref | Expression |
---|---|
iinab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2281 | . . . 4 | |
2 | nfab1 2283 | . . . 4 | |
3 | 1, 2 | nfiinxy 3840 | . . 3 |
4 | nfab1 2283 | . . 3 | |
5 | 3, 4 | cleqf 2305 | . 2 |
6 | abid 2127 | . . . 4 | |
7 | 6 | ralbii 2441 | . . 3 |
8 | vex 2689 | . . . 4 | |
9 | eliin 3818 | . . . 4 | |
10 | 8, 9 | ax-mp 5 | . . 3 |
11 | abid 2127 | . . 3 | |
12 | 7, 10, 11 | 3bitr4i 211 | . 2 |
13 | 5, 12 | mpgbir 1429 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1331 wcel 1480 cab 2125 wral 2416 cvv 2686 ciin 3814 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-v 2688 df-iin 3816 |
This theorem is referenced by: iinrabm 3875 |
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