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Theorem r19.3rm 3289
Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 19-Dec-2018.)
Hypothesis
Ref Expression
r19.3rm.1  F/
Assertion
Ref Expression
r19.3rm
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem r19.3rm
Dummy variable  a is distinct from all other variables.
StepHypRef Expression
1 eleq1 2082 . . 3  a 
a
21cbvexv 1777 . 2  a  a
3 eleq1 2082 . . . 4  a 
a
43cbvexv 1777 . . 3  a  a
5 biimt 230 . . . 4
6 df-ral 2289 . . . . 5
7 r19.3rm.1 . . . . . 6  F/
8719.23 1550 . . . . 5
96, 8bitri 173 . . . 4
105, 9syl6bbr 187 . . 3
114, 10sylbi 114 . 2  a  a
122, 11sylbir 125 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1226   F/wnf 1329  wex 1362   wcel 1374  wral 2284
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-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-cleq 2015  df-clel 2018  df-ral 2289
This theorem is referenced by:  r19.3rmv  3290
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