Theorem ecase23d 1332

Description: Deduction for elimination by cases. (Contributed by NM, 22-Apr-1994.)

Hypotheses

Ref	Expression
ecase23d.1
ecase23d.2
ecase23d.3

Assertion

Ref	Expression
ecase23d

Proof of Theorem ecase23d

Step	Hyp	Ref	Expression
1		ecase23d.1	. . 3
2		ecase23d.2	. . 3
3		ioran 490	. . 3
4	1, 2, 3	sylanbrc 664	. 2
5		ecase23d.3	. . . 4
6		3orass 976	. . . 4
7	5, 6	sylib 196	. . 3
8	7	ord 377	. 2
9	4, 8	mt3d 125	1

Syntax hints:  -.wn 3  ->wi 4  \/wo 368  \/w3o 972

This theorem is referenced by:  tz7.7  4909  archiabllem2b  27740  wfrlem10  29352

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  df-3or 974