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Theorem rabasiun 4334
Description: A class abstraction with a restricted existential quantification expressed as indexed union. (Contributed by Alexander van der Vekens, 29-Jul-2018.)
Assertion
Ref Expression
rabasiun
Distinct variable groups:   , ,   , ,

Proof of Theorem rabasiun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfcv 2619 . . . . . 6
21nfcri 2612 . . . . 5
3 nfv 1707 . . . . 5
42, 3nfan 1928 . . . 4
5 nfcv 2619 . . . . . 6
65nfcri 2612 . . . . 5
7 nfcv 2619 . . . . . 6
8 nfs1v 2181 . . . . . 6
97, 8nfrex 2920 . . . . 5
106, 9nfan 1928 . . . 4
11 eleq1 2529 . . . . 5
12 sbequ12 1992 . . . . . 6
1312rexbidv 2968 . . . . 5
1411, 13anbi12d 710 . . . 4
154, 10, 14cbvab 2598 . . 3
16 r19.42v 3012 . . . . 5
17 nfcv 2619 . . . . . . . 8
1817, 5, 8, 12elrabf 3255 . . . . . . 7
1918bicomi 202 . . . . . 6
2019rexbii 2959 . . . . 5
2116, 20bitr3i 251 . . . 4
2221abbii 2591 . . 3
2315, 22eqtri 2486 . 2
24 df-rab 2816 . 2
25 df-iun 4332 . 2
2623, 24, 253eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  =wceq 1395  [wsb 1739  e.wcel 1818  {cab 2442  E.wrex 2808  {crab 2811  U_ciun 4330
This theorem is referenced by:  hashrabrex  13637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-iun 4332
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