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Theorem ssabral 3406
 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:   ,
Allowed substitution hint:   ()

Proof of Theorem ssabral
StepHypRef Expression
1 ssab 3405 . 2
2 df-ral 2702 . 2
31, 2bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wcel 1725  cab 2421  wral 2697   wss 3312 This theorem is referenced by:  txdis1cn  17659  divstgplem  18142  xrhmeo  18963  cncmet  19267  itg1addlem4  19583  subfacp1lem6  24863  comppfsc  26378  istotbnd3  26471  sstotbnd  26475  heibor1lem  26509  heibor1  26510 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-in 3319  df-ss 3326
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