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Theorem ssab2 3570
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 455 . 2  |-  ( ( x  e.  A  /\  ph )  ->  x  e.  A )
21abssi 3561 1  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  A
Colors of variables: wff setvar class
Syntax hints:    /\ wa 367    e. wcel 1823   {cab 2439    C_ wss 3461
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-in 3468  df-ss 3475
This theorem is referenced by:  ssrab2  3571  zfausab  4586  exss  4700  dmopabss  5203  fabexg  6729  isf32lem9  8732  psubspset  35865  psubclsetN  36057
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