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

Theorem sbcng 3201
 Description: Move negation in and out of class substitution. (Contributed by NM, 16-Jan-2004.)
Assertion
Ref Expression
sbcng

Proof of Theorem sbcng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3164 . 2
2 dfsbcq2 3164 . . 3
32notbid 286 . 2
4 sbn 2130 . 2
51, 3, 4vtoclbg 3012 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wceq 1652  wsb 1658   wcel 1725  wsbc 3161 This theorem is referenced by:  sbcrext  3234  sbcnel12g  3268  sbcne12g  3269  difopab  5006  onfrALTlem5  28628  onfrALTlem5VD  28997  bnj23  29083  bnj110  29229  bnj1204  29381 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162
 Copyright terms: Public domain W3C validator