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Mirrors > Home > NFE Home > Th. List > rexun | Unicode version |
Description: Restricted existential quantification over union. (Contributed by Jeff Madsen, 5-Jan-2011.) |
Ref | Expression |
---|---|
rexun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2620 | . 2 | |
2 | 19.43 1605 | . . 3 | |
3 | elun 3220 | . . . . . 6 | |
4 | 3 | anbi1i 676 | . . . . 5 |
5 | andir 838 | . . . . 5 | |
6 | 4, 5 | bitri 240 | . . . 4 |
7 | 6 | exbii 1582 | . . 3 |
8 | df-rex 2620 | . . . 4 | |
9 | df-rex 2620 | . . . 4 | |
10 | 8, 9 | orbi12i 507 | . . 3 |
11 | 2, 7, 10 | 3bitr4i 268 | . 2 |
12 | 1, 11 | bitri 240 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wo 357 wa 358 wex 1541 wcel 1710 wrex 2615 cun 3207 |
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-nan 1288 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-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 |
This theorem is referenced by: rexprg 3776 rextpg 3778 iunxun 4047 pw1un 4163 nnadjoin 4520 tfinnn 4534 phiun 4614 |
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