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Theorem nfiu1 3879
 Description: Bound-variable hypothesis builder for indexed union. (Contributed by NM, 12-Oct-2003.)
Assertion
Ref Expression
nfiu1 𝑥 𝑥𝐴 𝐵

Proof of Theorem nfiu1
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 df-iun 3851 . 2 𝑥𝐴 𝐵 = {𝑦 ∣ ∃𝑥𝐴 𝑦𝐵}
2 nfre1 2500 . . 3 𝑥𝑥𝐴 𝑦𝐵
32nfab 2304 . 2 𝑥{𝑦 ∣ ∃𝑥𝐴 𝑦𝐵}
41, 3nfcxfr 2296 1 𝑥 𝑥𝐴 𝐵
 Colors of variables: wff set class Syntax hints:   ∈ wcel 2128  {cab 2143  Ⅎwnfc 2286  ∃wrex 2436  ∪ ciun 3849 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-iun 3851 This theorem is referenced by:  ssiun2s  3893  triun  4075  eliunxp  4724  opeliunxp2  4725  opeliunxp2f  6182  ixpf  6662  ctiunctlemfo  12151
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