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Theorem rabssab 3432
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 2716 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 simpr 449 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ph )
32ss2abi 3417 . 2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  { x  | 
ph }
41, 3eqsstri 3380 1  |-  { x  e.  A  |  ph }  C_ 
{ x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 360    e. wcel 1726   {cab 2424   {crab 2711    C_ wss 3322
This theorem is referenced by:  epse  4567  riotasbc  6567  aannenlem2  20248  aalioulem2  20252  ballotlemfmpn  24754  rencldnfilem  26883
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-rab 2716  df-in 3329  df-ss 3336
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