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Theorem nfiunxy 3834
 Description: Bound-variable hypothesis builder for indexed union. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiunxy.1
nfiunxy.2
Assertion
Ref Expression
nfiunxy
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem nfiunxy
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 3810 . 2
2 nfiunxy.1 . . . 4
3 nfiunxy.2 . . . . 5
43nfcri 2273 . . . 4
52, 4nfrexxy 2470 . . 3
65nfab 2284 . 2
71, 6nfcxfr 2276 1
 Colors of variables: wff set class Syntax hints:   wcel 1480  cab 2123  wnfc 2266  wrex 2415  ciun 3808 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-iun 3810 This theorem is referenced by:  iunab  3854
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