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Theorem rabssab 3272
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 2565 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 simpr 447 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ph )
32ss2abi 3258 . 2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  { x  | 
ph }
41, 3eqsstri 3221 1  |-  { x  e.  A  |  ph }  C_ 
{ x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 358    e. wcel 1696   {cab 2282   {crab 2560    C_ wss 3165
This theorem is referenced by:  riotasbc  6336  aannenlem2  19725  aalioulem2  19729
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-in 3172  df-ss 3179
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