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Theorem iinexg 4187
 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 3952 . . 3
3 elisset 2811 . . . . . . . . 9
43rgenw 2623 . . . . . . . 8
5 r19.2z 3556 . . . . . . . 8
64, 5mpan2 652 . . . . . . 7
7 r19.35 2700 . . . . . . 7
86, 7sylib 188 . . . . . 6
98imp 418 . . . . 5
10 rexcom4 2820 . . . . 5
119, 10sylib 188 . . . 4
12 abn0 3486 . . . 4
1311, 12sylibr 203 . . 3
14 intex 4183 . . 3
1513, 14sylib 188 . 2
162, 15eqeltrd 2370 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wex 1531   wceq 1632   wcel 1696  cab 2282   wne 2459  wral 2556  wrex 2557  cvv 2801  c0 3468  cint 3878  ciin 3922 This theorem is referenced by:  fclsval  17719  taylfval  19754  inttop2  25618 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-nul 3469  df-int 3879  df-iin 3924
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