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Theorem ssab2 3103
Description: Subclass relation for the restriction of a class abstraction. (Contributed by NM, 31-Mar-1995.)
Assertion
Ref Expression
ssab2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  A
Distinct variable group:    x, A
Allowed substitution hint:    ph( x)

Proof of Theorem ssab2
StepHypRef Expression
1 simpl 107 . 2  |-  ( ( x  e.  A  /\  ph )  ->  x  e.  A )
21abssi 3094 1  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  A
Colors of variables: wff set class
Syntax hints:    /\ wa 102    e. wcel 1438   {cab 2074    C_ wss 2997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-in 3003  df-ss 3010
This theorem is referenced by:  ssrab2  3104  zfausab  3973  exss  4045  dmopabss  4636  fabexg  5182
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