Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.54dc Unicode version

Theorem pm5.54dc 827
 Description: A conjunction is equivalent to one of its conjuncts, given a decidable conjunct. Based on theorem *5.54 of [WhiteheadRussell] p. 125. (Contributed by Jim Kingdon, 30-Mar-2018.)
Assertion
Ref Expression
pm5.54dc DECID

Proof of Theorem pm5.54dc
StepHypRef Expression
1 df-dc 743 . . 3 DECID
2 simpr 103 . . . . 5
3 ax-ia3 101 . . . . 5
42, 3impbid2 131 . . . 4
5 simpl 102 . . . . 5
6 ax-in2 545 . . . . 5
75, 6impbid2 131 . . . 4
84, 7orim12i 676 . . 3
91, 8sylbi 114 . 2 DECID
109orcomd 648 1 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-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