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Theorem predss 25451
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 25444 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 inss1 3563 . 2  |-  ( A  i^i  ( `' R " { X } ) )  C_  A
31, 2eqsstri 3380 1  |-  Pred ( R ,  A ,  X )  C_  A
Colors of variables: wff set class
Syntax hints:    i^i cin 3321    C_ wss 3322   {csn 3816   `'ccnv 4880   "cima 4884   Predcpred 25443
This theorem is referenced by:  predreseq  25459  trpredlem1  25510  wfr3g  25542  wfrlem4  25546  wfrlem10  25552  wsuclem  25581  frr3g  25586  frrlem4  25590
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-ss 3336  df-pred 25444
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