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Theorem bnj1149 28869
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1149.1  |-  ( ph  ->  A  e.  _V )
bnj1149.2  |-  ( ph  ->  B  e.  _V )
Assertion
Ref Expression
bnj1149  |-  ( ph  ->  ( A  u.  B
)  e.  _V )

Proof of Theorem bnj1149
StepHypRef Expression
1 bnj1149.1 . 2  |-  ( ph  ->  A  e.  _V )
2 bnj1149.2 . 2  |-  ( ph  ->  B  e.  _V )
3 unexg 4669 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  ->  ( A  u.  B
)  e.  _V )
41, 2, 3syl2anc 643 1  |-  ( ph  ->  ( A  u.  B
)  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721   _Vcvv 2916    u. cun 3278
This theorem is referenced by:  bnj1136  29072  bnj1413  29110  bnj1452  29127  bnj1489  29131
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363  ax-un 4660
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-rex 2672  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-sn 3780  df-pr 3781  df-uni 3976
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