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Theorem predss 24173
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 24168 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 inss1 3389 . 2  |-  ( A  i^i  ( `' R " { X } ) )  C_  A
31, 2eqsstri 3208 1  |-  Pred ( R ,  A ,  X )  C_  A
Colors of variables: wff set class
Syntax hints:    i^i cin 3151    C_ wss 3152   {csn 3640   `'ccnv 4688   "cima 4692   Predcpred 24167
This theorem is referenced by:  predreseq  24179  trpredlem1  24230  wfr3g  24255  wfrlem4  24259  wfrlem10  24265  frr3g  24280  frrlem4  24284
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166  df-pred 24168
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