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Theorem iinexg 4612
 Description: The existence of an indexed union. is normally a free-variable parameter in , which should be read (x). (Contributed by FL, 19-Sep-2011.)
Assertion
Ref Expression
iinexg
Distinct variable group:   ,

Proof of Theorem iinexg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfiin2g 4363 . . 3
3 elisset 3120 . . . . . . . . 9
43rgenw 2818 . . . . . . . 8
5 r19.2z 3918 . . . . . . . 8
64, 5mpan2 671 . . . . . . 7
7 r19.35 3004 . . . . . . 7
86, 7sylib 196 . . . . . 6
98imp 429 . . . . 5
10 rexcom4 3129 . . . . 5
119, 10sylib 196 . . . 4
12 abn0 3804 . . . 4
1311, 12sylibr 212 . . 3
14 intex 4608 . . 3
1513, 14sylib 196 . 2
162, 15eqeltrd 2545 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  =/=wne 2652  A.wral 2807  E.wrex 2808   cvv 3109   c0 3784  |^|cint 4286  |^|_ciin 4331 This theorem is referenced by:  fclsval  20509  taylfval  22754 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-sep 4573 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-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-int 4287  df-iin 4333
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