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Theorem unex 4176
 Description: The union of two sets is a set. Corollary 5.8 of [TakeutiZaring] p. 16. (Contributed by NM, 1-Jul-1994.)
Hypotheses
Ref Expression
unex.1
unex.2
Assertion
Ref Expression
unex

Proof of Theorem unex
StepHypRef Expression
1 unex.1 . . 3
2 unex.2 . . 3
31, 2unipr 3594 . 2
4 prexgOLD 3946 . . . 4
51, 2, 4mp2an 402 . . 3
65uniex 4174 . 2
73, 6eqeltrri 2111 1
 Colors of variables: wff set class Syntax hints:   wcel 1393  cvv 2557   cun 2915  cpr 3376  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-pr 3944  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-un 2922  df-sn 3381  df-pr 3382  df-uni 3581 This theorem is referenced by:  unexb  4177  rdg0  5974  unen  6293  findcard2  6346  findcard2s  6347  ac6sfi  6352  nn0ex  8187  xrex  8756
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