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Theorem iinexg 4556
 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 4306 . . 3
3 elisset 3072 . . . . . . . . 9
43rgenw 2767 . . . . . . . 8
5 r19.2z 3864 . . . . . . . 8
64, 5mpan2 671 . . . . . . 7
7 r19.35 2956 . . . . . . 7
86, 7sylib 198 . . . . . 6
98imp 429 . . . . 5
10 rexcom4 3081 . . . . 5
119, 10sylib 198 . . . 4
12 abn0 3760 . . . 4
1311, 12sylibr 214 . . 3
14 intex 4552 . . 3
1513, 14sylib 198 . 2
162, 15eqeltrd 2492 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1407  wex 1635   wcel 1844  cab 2389   wne 2600  wral 2756  wrex 2757  cvv 3061  c0 3740  cint 4229  ciin 4274 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-8 1846  ax-9 1848  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382  ax-sep 4519 This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ne 2602  df-ral 2761  df-rex 2762  df-v 3063  df-dif 3419  df-in 3423  df-ss 3430  df-nul 3741  df-int 4230  df-iin 4276 This theorem is referenced by:  fclsval  20803  taylfval  23048
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