Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  r19.32vdc Unicode version

Theorem r19.32vdc 2504
 Description: Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers, where is decidable. (Contributed by Jim Kingdon, 4-Jun-2018.)
Assertion
Ref Expression
r19.32vdc DECID
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem r19.32vdc
StepHypRef Expression
1 r19.21v 2439 . . 3
21a1i 9 . 2 DECID
3 dfordc 825 . . 3 DECID
43ralbidv 2369 . 2 DECID
5 dfordc 825 . 2 DECID
62, 4, 53bitr4d 218 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 103   wo 662  DECID wdc 776  wral 2349 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-dc 777  df-nf 1391  df-ral 2354 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator