Theorem sbc3angOLD 3391

Description: Distribution of class substitution over triple conjunction. (Contributed by NM, 14-Dec-2006.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) Obsolete as of 17-Aug-2018. Use sbc3an 3390 instead. (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
sbc3angOLD

Proof of Theorem sbc3angOLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfsbcq2 3330	. 2
2		dfsbcq2 3330	. . 3
3		dfsbcq2 3330	. . 3
4		dfsbcq2 3330	. . 3
5	2, 3, 4	3anbi123d 1299	. 2
6		sb3an 2141	. 2
7	1, 5, 6	vtoclbg 3168	1

Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327

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-3an 975  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