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Theorem rabssab 3154
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 2402 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 simpr 109 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ph )
32ss2abi 3139 . 2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  { x  | 
ph }
41, 3eqsstri 3099 1  |-  { x  e.  A  |  ph }  C_ 
{ x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    e. wcel 1465   {cab 2103   {crab 2397    C_ wss 3041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rab 2402  df-in 3047  df-ss 3054
This theorem is referenced by:  epse  4234  riotasbc  5713  genipv  7285  toponsspwpwg  12116  dmtopon  12117
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