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Theorem bj-rabtr 32765
Description: Restricted class abstraction with true formula. (Contributed by BJ, 22-Apr-2019.)
Assertion
Ref Expression
bj-rabtr  |-  { x  e.  A  | T.  }  =  A
Distinct variable group:    x, A

Proof of Theorem bj-rabtr
StepHypRef Expression
1 ssrab2 3546 . 2  |-  { x  e.  A  | T.  }  C_  A
2 ssid 3484 . . 3  |-  A  C_  A
3 tru 1374 . . . 4  |- T.
43rgenw 2901 . . 3  |-  A. x  e.  A T.
5 ssrab 3539 . . 3  |-  ( A 
C_  { x  e.  A  | T.  }  <->  ( A  C_  A  /\  A. x  e.  A T.  ) )
62, 4, 5mpbir2an 911 . 2  |-  A  C_  { x  e.  A  | T.  }
71, 6eqssi 3481 1  |-  { x  e.  A  | T.  }  =  A
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   T. wtru 1371   A.wral 2799   {crab 2803    C_ wss 3437
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-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2804  df-rab 2808  df-in 3444  df-ss 3451
This theorem is referenced by: (None)
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