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Theorem sqxpexg 7736
Description: The Cartesian square of a set is a set. (Contributed by AV, 13-Jan-2020.)
Assertion
Ref Expression
sqxpexg (𝐴𝑉 → (𝐴 × 𝐴) ∈ V)

Proof of Theorem sqxpexg
StepHypRef Expression
1 xpexg 7731 . 2 ((𝐴𝑉𝐴𝑉) → (𝐴 × 𝐴) ∈ V)
21anidms 566 1 (𝐴𝑉 → (𝐴 × 𝐴) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  Vcvv 3466   × cxp 5665
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pow 5354  ax-pr 5418  ax-un 7719
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-pw 4597  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-opab 5202  df-xp 5673  df-rel 5674
This theorem is referenced by:  resiexg  7899  erex  8724  hartogslem2  9535  harwdom  9583  dfac8b  10023  ac10ct  10026  canthwe  10643  cicer  17754  ssclem  17767  ipolerval  18489  dfrngc2  20516  dfringc2  20545  rngcresringcat  20557  mat0op  22245  matecl  22251  matlmod  22255  mattposvs  22281  ustval  24031  isust  24032  restutopopn  24067  ressuss  24091  ispsmet  24134  ismet  24153  isxmet  24154  satef  34898  satefvfmla0  34900  satefvfmla1  34907  fin2so  36969  rtrclexlem  42881  isclintop  47095  isassintop  47098  rngccofvalALTV  47158  ringccofvalALTV  47192  2arymaptf  47551
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