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Theorem r19.9rmv 3341
 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 2116 . . 3
21cbvexv 1811 . 2
3 eleq1 2116 . . . 4
43cbvexv 1811 . . 3
5 df-rex 2329 . . . . 5
6 19.41v 1798 . . . . 5
75, 6bitri 177 . . . 4
87baibr 840 . . 3
94, 8sylbi 118 . 2
102, 9sylbir 129 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wex 1397   wcel 1409  wrex 2324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-clel 2052  df-rex 2329 This theorem is referenced by:  r19.45mv  3343  iunconstm  3693  fconstfvm  5407  ltexprlemloc  6763
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