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

Step	Hyp	Ref	Expression
1		spsbcd.1	. 2
2		spsbcd.2	. 2
3		spsbc 3340	. 2
4	1, 2, 3	sylc 60	1

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