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Mirrors > Home > ILE 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 2399 | . 2 | |
2 | 19.43 1592 | . . 3 | |
3 | elun 3187 | . . . . . 6 | |
4 | 3 | anbi1i 453 | . . . . 5 |
5 | andir 793 | . . . . 5 | |
6 | 4, 5 | bitri 183 | . . . 4 |
7 | 6 | exbii 1569 | . . 3 |
8 | df-rex 2399 | . . . 4 | |
9 | df-rex 2399 | . . . 4 | |
10 | 8, 9 | orbi12i 738 | . . 3 |
11 | 2, 7, 10 | 3bitr4i 211 | . 2 |
12 | 1, 11 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wo 682 wex 1453 wcel 1465 wrex 2394 cun 3039 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 |
This theorem is referenced by: rexprg 3545 rextpg 3547 iunxun 3862 finexdc 6764 exfzdc 9972 |
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