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Theorem predss 29425
Description: The predecessor class of  A is a subset of  A. (Contributed by Scott Fenton, 2-Feb-2011.)
Assertion
Ref Expression
predss  |-  Pred ( R ,  A ,  X )  C_  A

Proof of Theorem predss
StepHypRef Expression
1 df-pred 29418 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 inss1 3714 . 2  |-  ( A  i^i  ( `' R " { X } ) )  C_  A
31, 2eqsstri 3529 1  |-  Pred ( R ,  A ,  X )  C_  A
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3470    C_ wss 3471   {csn 4032   `'ccnv 5007   "cima 5011   Predcpred 29417
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-in 3478  df-ss 3485  df-pred 29418
This theorem is referenced by:  predreseq  29433  trpredlem1  29484  wfr3g  29516  wfrlem4  29520  wfrlem10  29526  wsuclem  29555  frr3g  29560  frrlem4  29564
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