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Theorem bnj1149 28824
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 4521 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  ->  ( A  u.  B
)  e.  _V )
41, 2, 3syl2anc 642 1  |-  ( ph  ->  ( A  u.  B
)  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   _Vcvv 2788    u. cun 3150
This theorem is referenced by:  bnj1136  29027  bnj1413  29065  bnj1452  29082  bnj1489  29086
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rex 2549  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-pr 3647  df-uni 3828
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