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Theorem rabssab 3259
Description: A restricted class is a subclass of the corresponding unrestricted class. (Contributed by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
rabssab  |-  { x  e.  A  |  ph }  C_ 
{ x  |  ph }

Proof of Theorem rabssab
StepHypRef Expression
1 df-rab 2552 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 simpr 447 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ph )
32ss2abi 3245 . 2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  { x  | 
ph }
41, 3eqsstri 3208 1  |-  { x  e.  A  |  ph }  C_ 
{ x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 358    e. wcel 1684   {cab 2269   {crab 2547    C_ wss 3152
This theorem is referenced by:  riotasbc  6320  aannenlem2  19709  aalioulem2  19713
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-rab 2552  df-in 3159  df-ss 3166
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