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Theorem predasetex 27777
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 27761 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 predasetex.1 . . 3  |-  A  e. 
_V
32inex1 4533 . 2  |-  ( A  i^i  ( `' R " { X } ) )  e.  _V
41, 3eqeltri 2535 1  |-  Pred ( R ,  A ,  X )  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758   _Vcvv 3070    i^i cin 3427   {csn 3977   `'ccnv 4939   "cima 4943   Predcpred 27760
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 1952  ax-ext 2430  ax-sep 4513
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-v 3072  df-in 3435  df-pred 27761
This theorem is referenced by: (None)
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