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Theorem spsbc 2827
 Description: Specialization: if a formula is true for all sets, it is true for any class which is a set. Similar to Theorem 6.11 of [Quine] p. 44. See also stdpc4 1699 and rspsbc 2897. (Contributed by NM, 16-Jan-2004.)
Assertion
Ref Expression
spsbc

Proof of Theorem spsbc
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 stdpc4 1699 . . . 4
2 sbsbc 2820 . . . 4
31, 2sylib 120 . . 3
4 dfsbcq 2818 . . 3
53, 4syl5ib 152 . 2
65vtocleg 2670 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1283   wceq 1285   wcel 1434  wsb 1686  wsbc 2816 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-v 2604  df-sbc 2817 This theorem is referenced by:  spsbcd  2828  sbcth  2829  sbcthdv  2830  sbceqal  2870  sbcimdv  2880  csbiebt  2943  csbexga  3914
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