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Theorem uniexg 4175
 Description: The ZF Axiom of Union in class notation, in the form of a theorem instead of an inference. We use the antecedent instead of to make the theorem more general and thus shorten some proofs; obviously the universal class constant is one possible substitution for class variable . (Contributed by NM, 25-Nov-1994.)
Assertion
Ref Expression
uniexg

Proof of Theorem uniexg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 unieq 3589 . . 3
21eleq1d 2106 . 2
3 vex 2560 . . 3
43uniex 4174 . 2
52, 4vtoclg 2613 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  cvv 2557  cuni 3580 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-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-un 4170 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-uni 3581 This theorem is referenced by:  snnex  4181  uniexb  4205  ssonuni  4214  dmexg  4596  rnexg  4597  elxp4  4808  elxp5  4809  relrnfvex  5193  fvexg  5194  sefvex  5196  riotaexg  5472  iunexg  5746  1stvalg  5769  2ndvalg  5770  cnvf1o  5846  brtpos2  5866  tfrlemiex  5945  en1bg  6280  en1uniel  6284
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