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Theorem nfiun 4359
 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 4333 . 2
2 nfiun.1 . . . 4
3 nfiun.2 . . . . 5
43nfcri 2622 . . . 4
52, 4nfrex 2930 . . 3
65nfab 2633 . 2
71, 6nfcxfr 2627 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1767  cab 2452  wnfc 2615  wrex 2818  ciun 4331 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2822  df-rex 2823  df-iun 4333 This theorem is referenced by:  iunab  4377  disjxiun  4450  ovoliunnul  21786  iundisjf  27271  iundisj2f  27272  iundisjfi  27424  iundisj2fi  27425  trpredlem1  29237  trpredrec  29248  bnj1498  33597
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