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

Theorem predasetex 25394
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 25382 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 predasetex.1 . . 3  |-  A  e. 
_V
32inex1 4304 . 2  |-  ( A  i^i  ( `' R " { X } ) )  e.  _V
41, 3eqeltri 2474 1  |-  Pred ( R ,  A ,  X )  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1721   _Vcvv 2916    i^i cin 3279   {csn 3774   `'ccnv 4836   "cima 4840   Predcpred 25381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918  df-in 3287  df-pred 25382
  Copyright terms: Public domain W3C validator