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Theorem bj-xpexg2 33815
Description: Exported form (curried form) of xpexg 6587. (Contributed by BJ, 2-Apr-2019.)
Assertion
Ref Expression
bj-xpexg2  |-  ( A  e.  V  ->  ( B  e.  W  ->  ( A  X.  B )  e.  _V ) )

Proof of Theorem bj-xpexg2
StepHypRef Expression
1 xpexg 6587 . 2  |-  ( ( A  e.  V  /\  B  e.  W )  ->  ( A  X.  B
)  e.  _V )
21ex 434 1  |-  ( A  e.  V  ->  ( B  e.  W  ->  ( A  X.  B )  e.  _V ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1767   _Vcvv 3113    X. cxp 4997
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pow 4625  ax-pr 4686  ax-un 6577
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-rex 2820  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-pw 4012  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-opab 4506  df-xp 5005
This theorem is referenced by:  bj-xpnzexb  33816  bj-xtagex  33845
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