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Theorem predss 27654
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 27647 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 inss1 3591 . 2  |-  ( A  i^i  ( `' R " { X } ) )  C_  A
31, 2eqsstri 3407 1  |-  Pred ( R ,  A ,  X )  C_  A
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3348    C_ wss 3349   {csn 3898   `'ccnv 4860   "cima 4864   Predcpred 27646
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-v 2995  df-in 3356  df-ss 3363  df-pred 27647
This theorem is referenced by:  predreseq  27662  trpredlem1  27713  wfr3g  27745  wfrlem4  27749  wfrlem10  27755  wsuclem  27784  frr3g  27789  frrlem4  27793
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