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Theorem iunex 6780
 Description: The existence of an indexed union. is normally a free-variable parameter in the class expression substituted for , which can be read informally as (x). (Contributed by NM, 13-Oct-2003.)
Hypotheses
Ref Expression
iunex.1
iunex.2
Assertion
Ref Expression
iunex
Distinct variable group:   ,

Proof of Theorem iunex
StepHypRef Expression
1 iunex.1 . 2
2 iunex.2 . . 3
32rgenw 2818 . 2
4 iunexg 6776 . 2
51, 3, 4mp2an 672 1
 Colors of variables: wff setvar class Syntax hints:  e.wcel 1818  A.wral 2807   cvv 3109  U_ciun 4330 This theorem is referenced by:  abrexex2  6781  tz9.1  8181  tz9.1c  8182  cplem2  8329  fseqdom  8428  pwsdompw  8605  cfsmolem  8671  ac6c4  8882  konigthlem  8964  alephreg  8978  pwfseqlem4  9061  pwfseqlem5  9062  pwxpndom2  9064  wunex2  9137  wuncval2  9146  inar1  9174  isfunc  15233  dfac14  20119  txcmplem2  20143  cnextfval  20562  dfrtrclrec2  29066  rtrclreclem.refl  29067  rtrclreclem.subset  29068  rtrclreclem.min  29070  colinearex  29710  volsupnfl  30059  heiborlem3  30309  bnj893  33986 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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-rep 4563  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-fv 5601
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