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Theorem spsbcd 3341
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 2094 and rspsbc 3417. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
spsbcd.1
spsbcd.2
Assertion
Ref Expression
spsbcd

Proof of Theorem spsbcd
StepHypRef Expression
1 spsbcd.1 . 2
2 spsbcd.2 . 2
3 spsbc 3340 . 2
41, 2, 3sylc 60 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393  e.wcel 1818  [.wsbc 3327
This theorem is referenced by:  ovmpt2dxf  6428  ex-natded9.26  25140  spsbcdi  30523  ovmpt2rdxf  32928
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328
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