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Theorem ssrab2 3351
 Description: Subclass relation for a restricted class. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
ssrab2 {x A φ} A
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem ssrab2
StepHypRef Expression
1 df-rab 2623 . 2 {x A φ} = {x (x A φ)}
2 ssab2 3350 . 2 {x (x A φ)} A
31, 2eqsstri 3301 1 {x A φ} A
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   ∈ wcel 1710  {cab 2339  {crab 2618   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  iinrab2  4029  riinrab  4041  reiotacl  4364  nenpw1pwlem2  6085
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