Theorem imp_replast ≪ | index | src | ≫

\imp继位

theorem imp_replast (A B C D: wff):
  $ (A \imp B \imp C) \imp (C \imp D) \imp A \imp B \imp D $;
StepHypRefExpression
1 imp_imp_swapl 
((C \imp D) \imp (A \imp B \imp C) \imp A \imp B \imp D) \imp (A \imp B \imp C) \imp (C \imp D) \imp A \imp B \imp D
2 imp_tran 
((C \imp D) \imp (B \imp C) \imp B \imp D) \imp
  (((B \imp C) \imp B \imp D) \imp (A \imp B \imp C) \imp A \imp B \imp D) \imp
  (C \imp D) \imp
  (A \imp B \imp C) \imp
  A \imp
  B \imp
  D
3 imp_introl_imp 
(C \imp D) \imp (B \imp C) \imp B \imp D
4 2, 3 ax_mp 
(((B \imp C) \imp B \imp D) \imp (A \imp B \imp C) \imp A \imp B \imp D) \imp (C \imp D) \imp (A \imp B \imp C) \imp A \imp B \imp D
5 imp_introl_imp 
((B \imp C) \imp B \imp D) \imp (A \imp B \imp C) \imp A \imp B \imp D
6 4, 5 ax_mp 
(C \imp D) \imp (A \imp B \imp C) \imp A \imp B \imp D
7 1, 6 ax_mp 
(A \imp B \imp C) \imp (C \imp D) \imp A \imp B \imp D

Axiom use

Logic (ax_mp, ax_1, ax_2)