Theorem elimdhyp 4005

Description: Version of elimhyp 4000 where the hypothesis is deduced from the final antecedent. See ghomgrplem 29029 for an example of its use. (Contributed by Paul Chapman, 25-Mar-2008.)

Hypotheses

Ref	Expression
elimdhyp.1
elimdhyp.2
elimdhyp.3
elimdhyp.4

Assertion

Ref	Expression
elimdhyp

Proof of Theorem elimdhyp

Step	Hyp	Ref	Expression
1		elimdhyp.1	. . 3
2		iftrue 3947	. . . . 5
3	2	eqcomd 2465	. . . 4
4		elimdhyp.2	. . . 4
5	3, 4	syl 16	. . 3
6	1, 5	mpbid 210	. 2
7		elimdhyp.4	. . 3
8		iffalse 3950	. . . . 5
9	8	eqcomd 2465	. . . 4
10		elimdhyp.3	. . . 4
11	9, 10	syl 16	. . 3
12	7, 11	mpbii 211	. 2
13	6, 12	pm2.61i 164	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  ifcif 3941

This theorem is referenced by:  divalg  14061  ghomgrplem  29029

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