Theorem sbc8g 3335

Description: This is the closest we can get to df-sbc 3328 if we start from dfsbcq 3329 (see its comments) and dfsbcq2 3330. (Contributed by NM, 18-Nov-2008.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) (Proof modification is discouraged.)

Assertion

Ref	Expression
sbc8g

Proof of Theorem sbc8g

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfsbcq 3329	. 2
2		eleq1 2529	. 2
3		df-clab 2443	. . 3
4		equid 1791	. . . 4
5		dfsbcq2 3330	. . . 4
6	4, 5	ax-mp 5	. . 3
7	3, 6	bitr2i 250	. 2
8	1, 2, 7	vtoclbg 3168	1

Syntax hints:  ->wi 4  <->wb 184  [wsb 1739  e.wcel 1818  {cab 2442  [.wsbc 3327

This theorem is referenced by:  rusbcALT  31346  bnj984  34010

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-ext 2435

This theorem depends on definitions:  df-bi 185  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