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Theorem rexun 3123

Description: Restricted existential quantification over union. (Contributed by Jeff Madsen, 5-Jan-2011.)

**Assertion**
Ref	Expression
rexun	$\/$

**Proof of Theorem rexun**
Step	Hyp	Ref	Expression
1		df-rex 2312	. 2 $/\$
2		19.43 1519	. . 3 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
3		elun 3084	. . . . . 6 $\/$
4	3	anbi1i 431	. . . . 5 $/\$ $\/$ $/\$
5		andir 732	. . . . 5 $\/$ $/\$ $/\$ $\/$ $/\$
6	4, 5	bitri 173	. . . 4 $/\$ $/\$ $\/$ $/\$
7	6	exbii 1496	. . 3 $/\$ $/\$ $\/$ $/\$
8		df-rex 2312	. . . 4 $/\$
9		df-rex 2312	. . . 4 $/\$
10	8, 9	orbi12i 681	. . 3 $\/$ $/\$ $\/$ $/\$
11	2, 7, 10	3bitr4i 201	. 2 $/\$ $\/$
12	1, 11	bitri 173	1 $\/$

Colors of variables: wff set class

Syntax hints: $/\$ wa 97

wb 98 $\/$ wo 629

wex 1381

wcel 1393

wrex 2307

cun 2915

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022

This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922

This theorem is referenced by: rexprg 3422 rextpg 3424 iunxun 3735