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Mirrors > Home > NFE Home > Th. List > iunab | Unicode version |
Description: The indexed union of a class abstraction. (Contributed by NM, 27-Dec-2004.) |
Ref | Expression |
---|---|
iunab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2489 | . . . 4 | |
2 | nfab1 2491 | . . . 4 | |
3 | 1, 2 | nfiun 3995 | . . 3 |
4 | nfab1 2491 | . . 3 | |
5 | 3, 4 | cleqf 2513 | . 2 |
6 | abid 2341 | . . . 4 | |
7 | 6 | rexbii 2639 | . . 3 |
8 | eliun 3973 | . . 3 | |
9 | abid 2341 | . . 3 | |
10 | 7, 8, 9 | 3bitr4i 268 | . 2 |
11 | 5, 10 | mpgbir 1550 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wceq 1642 wcel 1710 cab 2339 wrex 2615 ciun 3969 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rex 2620 df-v 2861 df-iun 3971 |
This theorem is referenced by: iunrab 4013 iunid 4021 dfimafn2 5367 |
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