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Theorem ssabral 3537
Description: The relation for a subclass of a class abstraction is equivalent to restricted quantification. (Contributed by NM, 6-Sep-2006.)
Assertion
Ref Expression
ssabral
Distinct variable group:   ,

Proof of Theorem ssabral
StepHypRef Expression
1 ssab 3536 . 2
2 df-ral 2805 . 2
31, 2bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1368  e.wcel 1758  {cab 2439  A.wral 2800  C_wss 3442
This theorem is referenced by:  txdis1cn  19607  divstgplem  20090  xrhmeo  20917  cncmet  21232  itg1addlem4  21577  subfacp1lem6  27529  comppfsc  29039  istotbnd3  29130  sstotbnd  29134  heibor1lem  29168  heibor1  29169
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2805  df-in 3449  df-ss 3456
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