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Theorem nfiun 4358
 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 4332 . 2
2 nfiun.1 . . . 4
3 nfiun.2 . . . . 5
43nfcri 2612 . . . 4
52, 4nfrex 2920 . . 3
65nfab 2623 . 2
71, 6nfcxfr 2617 1
 Colors of variables: wff setvar class Syntax hints:  e.wcel 1818  {cab 2442  F/_wnfc 2605  E.wrex 2808  U_ciun 4330 This theorem is referenced by:  iunab  4376  disjxiun  4449  ovoliunnul  21918  iundisjf  27448  iundisj2f  27449  iundisjfi  27601  iundisj2fi  27602  trpredlem1  29310  trpredrec  29321  bnj1498  34117 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-iun 4332
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