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Theorem bnj1149 29237
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 4713 . 2  |-  ( ( A  e.  _V  /\  B  e.  _V )  ->  ( A  u.  B
)  e.  _V )
41, 2, 3syl2anc 644 1  |-  ( ph  ->  ( A  u.  B
)  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726   _Vcvv 2958    u. cun 3320
This theorem is referenced by:  bnj1136  29440  bnj1413  29478  bnj1452  29495  bnj1489  29499
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406  ax-un 4704
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rex 2713  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-sn 3822  df-pr 3823  df-uni 4018
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