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Theorem r19.28mv 3308
 Description: Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. It is valid only when the domain of quantification is inhabited. (Contributed by Jim Kingdon, 6-Aug-2018.)
Assertion
Ref Expression
r19.28mv (x x A → (x A (φ ψ) ↔ (φ x A ψ)))
Distinct variable groups:   x,A   φ,x
Allowed substitution hint:   ψ(x)

Proof of Theorem r19.28mv
StepHypRef Expression
1 nfv 1418 . 2 xφ
21r19.28m 3305 1 (x x A → (x A (φ ψ) ↔ (φ x A ψ)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ 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:  iinrabm  3710  iindif2m  3715  iinin2m  3716  xpiindim  4416  fintm  5018
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