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

Theorem 3orim123d 1263
 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 813 . . 3
4 3anim123d.3 . . 3
53, 4orim12d 813 . 2
6 df-3or 938 . 2
7 df-3or 938 . 2
85, 6, 73imtr4g 263 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   w3o 936 This theorem is referenced by:  fr3nr  4795  soxp  6495  zorn2lem6  8419  fpwwe2lem12  8554  fpwwe2lem13  8555  sltres  25654  colinearalglem4  25883  colinearxfr  26044 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 179  df-or 361  df-an 362  df-3or 938
 Copyright terms: Public domain W3C validator