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Theorem bnj1149 28586
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 4603 . 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 1710   _Vcvv 2864    u. cun 3226
This theorem is referenced by:  bnj1136  28789  bnj1413  28827  bnj1452  28844  bnj1489  28848
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-13 1712  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4222  ax-nul 4230  ax-pr 4295  ax-un 4594
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-rex 2625  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-sn 3722  df-pr 3723  df-uni 3909
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