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Theorem sqxpexg 4760
Description: The Cartesian square of a set is a set. (Contributed by AV, 13-Jan-2020.)
Assertion
Ref Expression
sqxpexg  |-  ( A  e.  V  ->  ( A  X.  A )  e. 
_V )

Proof of Theorem sqxpexg
StepHypRef Expression
1 xpexg 4758 . 2  |-  ( ( A  e.  V  /\  A  e.  V )  ->  ( A  X.  A
)  e.  _V )
21anidms 397 1  |-  ( A  e.  V  ->  ( A  X.  A )  e. 
_V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2160   _Vcvv 2752    X. cxp 4642
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4192  ax-pr 4227  ax-un 4451
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-opab 4080  df-xp 4650
This theorem is referenced by:  ispsmet  14280  ismet  14301  isxmet  14302  xmetunirn  14315
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