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Theorem spsbc 3058
 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 2024 and rspsbc 3124. (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 2024 . . . 4
2 sbsbc 3050 . . . 4
31, 2sylib 188 . . 3
4 dfsbcq 3048 . . 3
53, 4syl5ib 210 . 2
65vtocleg 2925 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1540   wceq 1642  wsb 1648   wcel 1710  wsbc 3046 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861  df-sbc 3047 This theorem is referenced by:  spsbcd  3059  sbcth  3060  sbcthdv  3061  sbceqal  3097  sbcimdv  3107  csbexg  3146  csbiebt  3172
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