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Theorem bj-projex 32785
Description: Sethood of the class projection. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-projex  |-  ( B  e.  V  ->  ( A Proj  B )  e.  _V )

Proof of Theorem bj-projex
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 df-bj-proj 32781 . 2  |-  ( A Proj 
B )  =  {
x  |  { x }  e.  ( B " { A } ) }
2 bj-clex 32754 . 2  |-  ( B  e.  V  ->  { x  |  { x }  e.  ( B " { A } ) }  e.  _V )
31, 2syl5eqel 2541 1  |-  ( B  e.  V  ->  ( A Proj  B )  e.  _V )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1758   {cab 2436   _Vcvv 3065   {csn 3972   "cima 4938   Proj bj-cproj 32780
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 1952  ax-ext 2430  ax-rep 4498  ax-sep 4508  ax-nul 4516  ax-pr 4626  ax-un 6469
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 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-ne 2644  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3067  df-sbc 3282  df-csb 3384  df-dif 3426  df-un 3428  df-in 3430  df-ss 3437  df-nul 3733  df-if 3887  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4187  df-br 4388  df-opab 4446  df-xp 4941  df-cnv 4943  df-dm 4945  df-rn 4946  df-res 4947  df-ima 4948  df-bj-proj 32781
This theorem is referenced by:  bj-pr1ex  32796  bj-pr2ex  32810
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