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Theorem rabssab 3235
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 2457 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 simpr 109 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ph )
32ss2abi 3219 . 2  |-  { x  |  ( x  e.  A  /\  ph ) }  C_  { x  | 
ph }
41, 3eqsstri 3179 1  |-  { x  e.  A  |  ph }  C_ 
{ x  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    e. wcel 2141   {cab 2156   {crab 2452    C_ wss 3121
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rab 2457  df-in 3127  df-ss 3134
This theorem is referenced by:  epse  4325  riotasbc  5821  genipv  7458  toponsspwpwg  12773  dmtopon  12774
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