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Theorem ssab2 3429
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 445 . 2  |-  ( ( x  e.  A  /\  ph )  ->  x  e.  A )
21abssi 3420 1  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  A
Colors of variables: wff set class
Syntax hints:    /\ wa 360    e. wcel 1726   {cab 2424    C_ wss 3322
This theorem is referenced by:  ssrab2  3430  zfausab  4354  exss  4428  dmopabss  5083  fabexg  5626  isf32lem9  8243  psubspset  30603  psubclsetN  30795
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-in 3329  df-ss 3336
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