Theorem 3orim123d 1307

Description: Deduction joining 3 implications to form implication of disjunctions. (Contributed by NM, 4-Apr-1997.)

Hypotheses

Ref	Expression
3anim123d.1
3anim123d.2
3anim123d.3

Assertion

Ref	Expression
3orim123d

Proof of Theorem 3orim123d

Step	Hyp	Ref	Expression
1		3anim123d.1	. . . 4
2		3anim123d.2	. . . 4
3	1, 2	orim12d 838	. . 3
4		3anim123d.3	. . 3
5	3, 4	orim12d 838	. 2
6		df-3or 974	. 2
7		df-3or 974	. 2
8	5, 6, 7	3imtr4g 270	1

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

This theorem is referenced by:  fr3nr  6615  soxp  6913  zorn2lem6  8902  fpwwe2lem12  9040  fpwwe2lem13  9041  colinearalglem4  24212  sltres  29424  colinearxfr  29725  fin2so  30040

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