Theorem sbcng 3368

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.

Step	Hyp	Ref	Expression
1		dfsbcq2 3330	. 2
2		dfsbcq2 3330	. . 3
3	2	notbid 294	. 2
4		sbn 2132	. 2
5	1, 3, 4	vtoclbg 3168	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327

This theorem is referenced by:  sbcn1  3375  sbcrextOLD  3409  sbcrext  3410  sbcnel12g  3826  sbcne12  3827  sbcne12gOLD  3828  difopab  5139  sbcni  30514  onfrALTlem5  33314  onfrALTlem5VD  33685  bnj23  33771  bnj110  33916  bnj1204  34068

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-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328