Theorem dedth4h 3996

Description: Weak deduction theorem eliminating four hypotheses. See comments in dedth2h 3994. (Contributed by NM, 16-May-1999.)

Hypotheses

Ref	Expression
dedth4h.1
dedth4h.2
dedth4h.3
dedth4h.4
dedth4h.5

Assertion

Ref	Expression
dedth4h

Proof of Theorem dedth4h

Step	Hyp	Ref	Expression
1		dedth4h.1	. . . 4
2	1	imbi2d 316	. . 3
3		dedth4h.2	. . . 4
4	3	imbi2d 316	. . 3
5		dedth4h.3	. . . 4
6		dedth4h.4	. . . 4
7		dedth4h.5	. . . 4
8	5, 6, 7	dedth2h 3994	. . 3
9	2, 4, 8	dedth2h 3994	. 2
10	9	imp 429	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  ifcif 3941

This theorem is referenced by:  dedth4v  3999  fprg  6080  omopth  7326  nn0opth2  12352  ax5seglem8  24239  hvsubsub4  25977  norm3lemt  26069  eigorth  26757

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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-if 3942