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Theorem bj-clex 32770
Description: Sethood of certain classes. (Contributed by BJ, 2-Apr-2019.)
Assertion
Ref Expression
bj-clex  |-  ( A  e.  V  ->  { x  |  { x }  e.  ( A " B ) }  e.  _V )
Distinct variable groups:    x, A    x, B
Allowed substitution hint:    V( x)

Proof of Theorem bj-clex
StepHypRef Expression
1 imaexg 6620 . 2  |-  ( A  e.  V  ->  ( A " B )  e. 
_V )
2 bj-snsetex 32769 . 2  |-  ( ( A " B )  e.  _V  ->  { x  |  { x }  e.  ( A " B ) }  e.  _V )
31, 2syl 16 1  |-  ( A  e.  V  ->  { x  |  { x }  e.  ( A " B ) }  e.  _V )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1758   {cab 2437   _Vcvv 3072   {csn 3980   "cima 4946
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431  ax-rep 4506  ax-sep 4516  ax-nul 4524  ax-pr 4634  ax-un 6477
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-fal 1376  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2265  df-mo 2266  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-ne 2647  df-ral 2801  df-rex 2802  df-rab 2805  df-v 3074  df-sbc 3289  df-csb 3391  df-dif 3434  df-un 3436  df-in 3438  df-ss 3445  df-nul 3741  df-if 3895  df-sn 3981  df-pr 3983  df-op 3987  df-uni 4195  df-br 4396  df-opab 4454  df-xp 4949  df-cnv 4951  df-dm 4953  df-rn 4954  df-res 4955  df-ima 4956
This theorem is referenced by:  bj-projex  32801
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