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Theorem iinexgm 3936
 Description: The existence of an indexed union. is normally a free-variable parameter in , which should be read . (Contributed by Jim Kingdon, 28-Aug-2018.)
Assertion
Ref Expression
iinexgm
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iinexgm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfiin2g 3718 . . 3
3 elisset 2585 . . . . . . . . . 10
43rgenw 2393 . . . . . . . . 9
5 r19.2m 3337 . . . . . . . . 9
64, 5mpan2 409 . . . . . . . 8
7 r19.35-1 2477 . . . . . . . 8
86, 7syl 14 . . . . . . 7
98imp 119 . . . . . 6
10 rexcom4 2594 . . . . . 6
119, 10sylib 131 . . . . 5
12 abid 2044 . . . . . 6
1312exbii 1512 . . . . 5
1411, 13sylibr 141 . . . 4
15 nfv 1437 . . . . 5
16 nfsab1 2046 . . . . 5
17 eleq1 2116 . . . . 5
1815, 16, 17cbvex 1655 . . . 4
1914, 18sylib 131 . . 3
20 inteximm 3931 . . 3
2119, 20syl 14 . 2
222, 21eqeltrd 2130 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wceq 1259  wex 1397   wcel 1409  cab 2042  wral 2323  wrex 2324  cvv 2574  cint 3643  ciin 3686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-in 2952  df-ss 2959  df-int 3644  df-iin 3688 This theorem is referenced by: (None)
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