Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  a4sbcd Unicode version

Theorem a4sbcd 2965
 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 1897 and ra4sbc 3030. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
a4sbcd.1
a4sbcd.2
Assertion
Ref Expression
a4sbcd

Proof of Theorem a4sbcd
StepHypRef Expression
1 a4sbcd.1 . 2
2 a4sbcd.2 . 2
3 a4sbc 2964 . 2
41, 2, 3sylc 58 1
 Colors of variables: wff set class Syntax hints:   wi 6  wal 1532   wcel 1621  wsbc 2952 This theorem is referenced by:  ex-natded9.26  20780 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-12o 1664  ax-9 1684  ax-4 1692  ax-ext 2237 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-v 2759  df-sbc 2953
 Copyright terms: Public domain W3C validator