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Theorem rexlimdv 2426
 Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 14-Nov-2002.) (Proof shortened by Eric Schmidt, 22-Dec-2006.)
Hypothesis
Ref Expression
rexlimdv.1 (φ → (x A → (ψχ)))
Assertion
Ref Expression
rexlimdv (φ → (x A ψχ))
Distinct variable groups:   φ,x   χ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem rexlimdv
StepHypRef Expression
1 nfv 1418 . 2 xφ
2 nfv 1418 . 2 xχ
3 rexlimdv.1 . 2 (φ → (x A → (ψχ)))
41, 2, 3rexlimd 2424 1 (φ → (x A ψχ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1390  ∃wrex 2301 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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306 This theorem is referenced by:  rexlimdva  2427  rexlimdv3a  2429  rexlimdvw  2430  rexlimdvv  2433  trintssm  3861  ssorduni  4179  funcnvuni  4911  dffo3  5257  smoiun  5857  tfrlem9  5876  axprecex  6744  recexap  7396  zdiv  8084  btwnz  8113  lbzbi  8307
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