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Theorem nfiu1 3678
 Description: Bound-variable hypothesis builder for indexed union. (Contributed by NM, 12-Oct-2003.)
Assertion
Ref Expression
nfiu1 x x A B

Proof of Theorem nfiu1
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-iun 3650 . 2 x A B = {yx A y B}
2 nfre1 2359 . . 3 xx A y B
32nfab 2179 . 2 x{yx A y B}
41, 3nfcxfr 2172 1 x x A B
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1390  {cab 2023  Ⅎwnfc 2162  ∃wrex 2301  ∪ ciun 3648 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-bndl 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-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-iun 3650 This theorem is referenced by:  ssiun2s  3692  triun  3858  eliunxp  4418  opeliunxp2  4419
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