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Theorem predasetex 23591
Description: The predecessor class exists when  A does. (Contributed by Scott Fenton, 8-Feb-2011.)
Hypothesis
Ref Expression
predasetex.1  |-  A  e. 
_V
Assertion
Ref Expression
predasetex  |-  Pred ( R ,  A ,  X )  e.  _V

Proof of Theorem predasetex
StepHypRef Expression
1 df-pred 23579 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 predasetex.1 . . 3  |-  A  e. 
_V
32inex1 4155 . 2  |-  ( A  i^i  ( `' R " { X } ) )  e.  _V
41, 3eqeltri 2353 1  |-  Pred ( R ,  A ,  X )  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   _Vcvv 2788    i^i cin 3151   {csn 3640   `'ccnv 4688   "cima 4692   Predcpred 23578
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-pred 23579
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