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Theorem nfiun 4119
 Description: Bound-variable hypothesis builder for indexed union. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiun.1
nfiun.2
Assertion
Ref Expression
nfiun

Proof of Theorem nfiun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 4095 . 2
2 nfiun.1 . . . 4
3 nfiun.2 . . . . 5
43nfcri 2566 . . . 4
52, 4nfrex 2761 . . 3
65nfab 2576 . 2
71, 6nfcxfr 2569 1
 Colors of variables: wff set class Syntax hints:   wcel 1725  cab 2422  wnfc 2559  wrex 2706  ciun 4093 This theorem is referenced by:  iunab  4137  disjxiun  4209  ovoliunnul  19403  iundisjf  24029  iundisj2f  24030  iundisjfi  24152  iundisj2fi  24153  trpredlem1  25505  trpredrec  25516  bnj1498  29430 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-iun 4095
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