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Theorem r19.3rm 3338
 Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 19-Dec-2018.)
Hypothesis
Ref Expression
r19.3rm.1
Assertion
Ref Expression
r19.3rm
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem r19.3rm
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 biimt 234 . . . 4
6 df-ral 2328 . . . . 5
7 r19.3rm.1 . . . . . 6
8719.23 1584 . . . . 5
96, 8bitri 177 . . . 4
105, 9syl6bbr 191 . . 3
114, 10sylbi 118 . 2
122, 11sylbir 129 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102  wal 1257  wnf 1365  wex 1397   wcel 1409  wral 2323 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-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-cleq 2049  df-clel 2052  df-ral 2328 This theorem is referenced by:  r19.28m  3339  r19.3rmv  3340  r19.27m  3344  indstr  8632
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