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Theorem eluni2 3575
Description: Membership in class union. Restricted quantifier version. (Contributed by NM, 31-Aug-1999.)
Assertion
Ref Expression
eluni2 (A Bx B A x)
Distinct variable groups:   x,A   x,B

Proof of Theorem eluni2
StepHypRef Expression
1 exancom 1496 . 2 (x(A x x B) ↔ x(x B A x))
2 eluni 3574 . 2 (A Bx(A x x B))
3 df-rex 2306 . 2 (x B A xx(x B A x))
41, 2, 33bitr4i 201 1 (A Bx B A x)
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wex 1378   wcel 1390  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-v 2553  df-uni 3572
This theorem is referenced by:  uni0b  3596  intssunim  3628  iuncom4  3655  inuni  3900  ssorduni  4179  unon  4202  cnvuni  4464  chfnrn  5221
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