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Theorem ssab2 3257
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 443 . 2  |-  ( ( x  e.  A  /\  ph )  ->  x  e.  A )
21abssi 3248 1  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  A
Colors of variables: wff set class
Syntax hints:    /\ wa 358    e. wcel 1684   {cab 2269    C_ wss 3152
This theorem is referenced by:  ssrab2  3258  zfausab  4163  exss  4236  dmopabss  4890  fabexg  5422  isf32lem9  7987  qusp  25542  psubspset  29933  psubclsetN  30125
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-in 3159  df-ss 3166
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