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Theorem predss 25387
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 25382 . 2  |-  Pred ( R ,  A ,  X )  =  ( A  i^i  ( `' R " { X } ) )
2 inss1 3521 . 2  |-  ( A  i^i  ( `' R " { X } ) )  C_  A
31, 2eqsstri 3338 1  |-  Pred ( R ,  A ,  X )  C_  A
Colors of variables: wff set class
Syntax hints:    i^i cin 3279    C_ wss 3280   {csn 3774   `'ccnv 4836   "cima 4840   Predcpred 25381
This theorem is referenced by:  predreseq  25393  trpredlem1  25444  wfr3g  25469  wfrlem4  25473  wfrlem10  25479  frr3g  25494  frrlem4  25498
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
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-ss 3294  df-pred 25382
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