Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  predasetex Structured version   Unicode version

Theorem predasetex 28687
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 28671 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 predasetex.1 . . 3  |-  A  e. 
_V
32inex1 4581 . 2  |-  ( A  i^i  ( `' R " { X } ) )  e.  _V
41, 3eqeltri 2544 1  |-  Pred ( R ,  A ,  X )  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1762   _Vcvv 3106    i^i cin 3468   {csn 4020   `'ccnv 4991   "cima 4995   Predcpred 28670
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-sep 4561
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-v 3108  df-in 3476  df-pred 28671
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator