Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm4.79dc Unicode version

Theorem pm4.79dc 809
 Description: Equivalence between a disjunction of two implications, and a conjunction and an implication. Based on theorem *4.79 of [WhiteheadRussell] p. 121 but with additional decidability antecedents. (Contributed by Jim Kingdon, 28-Mar-2018.)
Assertion
Ref Expression
pm4.79dc DECID DECID

Proof of Theorem pm4.79dc
StepHypRef Expression
1 id 19 . . . 4
2 id 19 . . . 4
31, 2jaoa 640 . . 3
4 simplimdc 757 . . . . . 6 DECID
5 pm3.3 248 . . . . . 6
64, 5syl9 66 . . . . 5 DECID
7 dcim 784 . . . . . 6 DECID DECID DECID
8 pm2.54dc 790 . . . . . 6 DECID
97, 8syl6 29 . . . . 5 DECID DECID
106, 9syl5d 62 . . . 4 DECID DECID
1110imp 115 . . 3 DECID DECID
123, 11impbid2 131 . 2 DECID DECID
1312expcom 109 1 DECID DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wb 98   wo 629  DECID wdc 742 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630 This theorem depends on definitions:  df-bi 110  df-dc 743 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator