Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  3orim123d Unicode version

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
StepHypRef Expression
1 3anim123d.1 . . . 4
2 3anim123d.2 . . . 4
31, 2orim12d 838 . . 3
4 3anim123d.3 . . 3
53, 4orim12d 838 . 2
6 df-3or 974 . 2
7 df-3or 974 . 2
85, 6, 73imtr4g 270 1
 Colors of variables: wff setvar class 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
 Copyright terms: Public domain W3C validator