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Theorem r19.3rmv 3290
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 1402 . 2 xφ
21r19.3rm 3289 1 (y y A → (φx A φ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  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:  iinconstm  3640  cnvpom  4787
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