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Theorem nfiu1 3681
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 3653 . 2 x A B = {yx A y B}
2 nfre1 2362 . . 3 xx A y B
32nfab 2182 . 2 x{yx A y B}
41, 3nfcxfr 2175 1 x x A B
Colors of variables: wff set class
Syntax hints:   wcel 1393  {cab 2026  wnfc 2165  wrex 2304   ciun 3651
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2309  df-iun 3653
This theorem is referenced by:  ssiun2s  3695  triun  3861  eliunxp  4421  opeliunxp2  4422
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