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Theorem iinexg 4360
 Description: The existence of an indexed union. is normally a free-variable parameter in , which should be read . (Contributed by FL, 19-Sep-2011.)
Assertion
Ref Expression
iinexg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iinexg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfiin2g 4124 . . 3
3 elisset 2966 . . . . . . . . 9
43rgenw 2773 . . . . . . . 8
5 r19.2z 3717 . . . . . . . 8
64, 5mpan2 653 . . . . . . 7
7 r19.35 2855 . . . . . . 7
86, 7sylib 189 . . . . . 6
98imp 419 . . . . 5
10 rexcom4 2975 . . . . 5
119, 10sylib 189 . . . 4
12 abn0 3646 . . . 4
1311, 12sylibr 204 . . 3
14 intex 4356 . . 3
1513, 14sylib 189 . 2
162, 15eqeltrd 2510 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2422   wne 2599  wral 2705  wrex 2706  cvv 2956  c0 3628  cint 4050  ciin 4094 This theorem is referenced by:  fclsval  18040  taylfval  20275 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-int 4051  df-iin 4096
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