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Theorem nfiinya 3727
 Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiunya.1
nfiunya.2
Assertion
Ref Expression
nfiinya
Distinct variable group:   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem nfiinya
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iin 3701 . 2
2 nfiunya.1 . . . 4
3 nfiunya.2 . . . . 5
43nfcri 2217 . . . 4
52, 4nfralya 2409 . . 3
65nfab 2227 . 2
71, 6nfcxfr 2220 1
 Colors of variables: wff set class Syntax hints:   wcel 1434  cab 2069  wnfc 2210  wral 2353  ciin 3699 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-iin 3701 This theorem is referenced by: (None)
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