Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  r19.9rmv Unicode version

Theorem r19.9rmv 3460
 Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 5-Aug-2018.)
Assertion
Ref Expression
r19.9rmv
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem r19.9rmv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2203 . . 3
21cbvexv 1891 . 2
3 eleq1 2203 . . . 4
43cbvexv 1891 . . 3
5 df-rex 2423 . . . . 5
6 19.41v 1875 . . . . 5
75, 6bitri 183 . . . 4
87baibr 906 . . 3
94, 8sylbi 120 . 2
102, 9sylbir 134 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wex 1469   wcel 1481  wrex 2418 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-clel 2136  df-rex 2423 This theorem is referenced by:  r19.45mv  3462  r19.44mv  3463  iunconstm  3830  fconstfvm  5647  frecabcl  6305  ltexprlemloc  7459  lcmgcdlem  11814
 Copyright terms: Public domain W3C validator