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Theorem ssrab2 3019
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 2309 . 2 {x Aφ} = {x ∣ (x A φ)}
2 ssab2 3018 . 2 {x ∣ (x A φ)} ⊆ A
31, 2eqsstri 2969 1 {x Aφ} ⊆ A
Colors of variables: wff set class
Syntax hints:   wa 97   wcel 1390  {cab 2023  {crab 2304  wss 2911
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309  df-in 2918  df-ss 2925
This theorem is referenced by:  ssrabeq  3020  rabexg  3891  pwnss  3903  ordtriexmidlem  4208  onsucsssucexmid  4212  onsucelsucexmidlem  4214  tfis  4249  nnregexmid  4285  dmmptss  4760  ssimaex  5177  f1oresrab  5272  riotacl  5425  ssfiexmid  6254  genpelxp  6494  ltexprlempr  6582  cauappcvgprlemcl  6625  cauappcvgprlemladd  6630  caucvgprlemcl  6647  uzf  8252  rpre  8364  ixxf  8537  fzf  8648  expcl2lemap  8921  expclzaplem  8933  expge0  8945  expge1  8946  bdrabexg  9361
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