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Theorem nfuni 3577
Description: Bound-variable hypothesis builder for union. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Hypothesis
Ref Expression
nfuni.1 xA
Assertion
Ref Expression
nfuni x A

Proof of Theorem nfuni
Dummy variables y z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfuni2 3573 . 2 A = {yz A y z}
2 nfuni.1 . . . 4 xA
3 nfv 1418 . . . 4 x y z
42, 3nfrexxy 2355 . . 3 xz A y z
54nfab 2179 . 2 x{yz A y z}
61, 5nfcxfr 2172 1 x A
Colors of variables: wff set class
Syntax hints:  {cab 2023  wnfc 2162  wrex 2301   cuni 3571
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-uni 3572
This theorem is referenced by:  nfiota1  4812  nfrecs  5863
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