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Theorem bj-xpexg2 31343
Description: Exported form (curried form) of xpexg 6598. (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 6598 . 2  |-  ( ( A  e.  V  /\  B  e.  W )  ->  ( A  X.  B
)  e.  _V )
21ex 435 1  |-  ( A  e.  V  ->  ( B  e.  W  ->  ( A  X.  B )  e.  _V ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1867   _Vcvv 3078    X. cxp 4843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-8 1869  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pow 4594  ax-pr 4652  ax-un 6588
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-pw 3978  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-opab 4476  df-xp 4851  df-rel 4852
This theorem is referenced by:  bj-xpnzexb  31344  bj-xtagex  31373
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