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Theorem rexlimdva 2409
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 20-Jan-2007.)
Hypothesis
Ref Expression
rexlimdva.1 ((φ x A) → (ψχ))
Assertion
Ref Expression
rexlimdva (φ → (x A ψχ))
Distinct variable groups:   φ,x   χ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem rexlimdva
StepHypRef Expression
1 rexlimdva.1 . . 3 ((φ x A) → (ψχ))
21ex 108 . 2 (φ → (x A → (ψχ)))
32rexlimdv 2408 1 (φ → (x A ψχ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1375  wrex 2283
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 1315  ax-gen 1317  ax-ie1 1362  ax-ie2 1363  ax-4 1382  ax-17 1401  ax-ial 1410  ax-i5r 1411
This theorem depends on definitions:  df-bi 110  df-nf 1329  df-ral 2287  df-rex 2288
This theorem is referenced by:  rexlimdvaa  2410  rexlimivv  2414  rexlimdvv  2415  ralxfrd  4117  rexxfrd  4118  fvelimab  5121  foco2  5210  elunirn  5297  f1elima  5304  tfrlem5  5817  tfrlemibacc  5826  tfrlemibfn  5828
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