Theorem dedth3v 3998

Description: Weak deduction theorem for eliminating a hypothesis with 3 class variables. See comments in dedth2v 3997. (Contributed by NM, 13-Aug-1999.) (Proof shortened by Eric Schmidt, 28-Jul-2009.)

Hypotheses

Ref	Expression
dedth3v.1
dedth3v.2
dedth3v.3
dedth3v.4

Assertion

Ref	Expression
dedth3v

Proof of Theorem dedth3v

Step	Hyp	Ref	Expression
1		dedth3v.1	. . . 4
2		dedth3v.2	. . . 4
3		dedth3v.3	. . . 4
4		dedth3v.4	. . . 4
5	1, 2, 3, 4	dedth3h 3995	. . 3
6	5	3anidm12 1285	. 2
7	6	anidms 645	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  ifcif 3941

This theorem is referenced by:  sseliALT  4583

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-11 1842  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-if 3942