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Theorem r19.3rmv 3306
Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 6-Aug-2018.)
Assertion
Ref Expression
r19.3rmv (y y A → (φx A φ))
Distinct variable groups:   x,A   y,A   φ,x
Allowed substitution hint:   φ(y)

Proof of Theorem r19.3rmv
StepHypRef Expression
1 nfv 1418 . 2 xφ
21r19.3rm 3304 1 (y y A → (φx A φ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wex 1378   wcel 1390  wral 2300
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033  df-ral 2305
This theorem is referenced by:  iinconstm  3657  cnvpom  4803  ssfiexmid  6254
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