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Theorem ssrab2 3002
Description: Subclass relation for a restricted class. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
ssrab2 {x Aφ} ⊆ A
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem ssrab2
StepHypRef Expression
1 df-rab 2293 . 2 {x Aφ} = {x ∣ (x A φ)}
2 ssab2 3001 . 2 {x ∣ (x A φ)} ⊆ A
31, 2eqsstri 2952 1 {x Aφ} ⊆ A
Colors of variables: wff set class
Syntax hints:   wa 97   wcel 1374  {cab 2008  {crab 2288  wss 2894
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rab 2293  df-in 2901  df-ss 2908
This theorem is referenced by:  ssrabeq  3003  rabexg  3874  pwnss  3886  ordtriexmidlem  4192  onsucsssucexmid  4196  onsucelsucexmidlem  4198  tfis  4233  nnregexmid  4269  dmmptss  4744  ssimaex  5159  f1oresrab  5254  riotacl  5406  genpelxp  6365  genpelpw  6371  ltexprlempr  6445  bdrabexg  7129
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