Theorem ecase2d 940

Description: Deduction for elimination by cases. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Dec-2012.)

Hypotheses

Ref	Expression
ecase2d.1
ecase2d.2
ecase2d.3
ecase2d.4

Assertion

Ref	Expression
ecase2d

Proof of Theorem ecase2d

Step	Hyp	Ref	Expression
1		idd 24	. 2
2		ecase2d.1	. . . 4
3		ecase2d.2	. . . . 5
4	3	pm2.21d 106	. . . 4
5	2, 4	mpand 675	. . 3
6		ecase2d.3	. . . . 5
7	6	pm2.21d 106	. . . 4
8	2, 7	mpand 675	. . 3
9	5, 8	jaod 380	. 2
10		ecase2d.4	. 2
11	1, 9, 10	mpjaod 381	1

Syntax hints:  -.wn 3  ->wi 4  \/wo 368  /\wa 369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371