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Theorem reximdv 2536
 Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998.)
Hypothesis
Ref Expression
reximdv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
reximdv (𝜑 → (∃𝑥𝐴 𝜓 → ∃𝑥𝐴 𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem reximdv
StepHypRef Expression
1 reximdv.1 . . 3 (𝜑 → (𝜓𝜒))
21a1d 22 . 2 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
32reximdvai 2535 1 (𝜑 → (∃𝑥𝐴 𝜓 → ∃𝑥𝐴 𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1481  ∃wrex 2418 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-ral 2422  df-rex 2423 This theorem is referenced by:  r19.12  2541  reusv3  4388  rexxfrd  4391  iunpw  4408  fvelima  5480  carden2bex  7061  prnmaddl  7321  prarloclem5  7331  prarloc2  7335  genprndl  7352  genprndu  7353  ltpopr  7426  recexprlemm  7455  recexprlemopl  7456  recexprlemopu  7458  recexprlem1ssl  7464  recexprlem1ssu  7465  cauappcvgprlemupu  7480  caucvgprlemupu  7503  caucvgprprlemupu  7531  caucvgsrlemoffres  7631  map2psrprg  7636  resqrexlemgt0  10823  subcn2  11111  bezoutlembz  11726  tgcl  12270  neiss  12356  ssnei2  12363  tgcnp  12415  cnptopco  12428  cnptopresti  12444  lmtopcnp  12456  blssexps  12635  blssex  12636  mopni3  12690  neibl  12697  metss  12700  metcnp3  12717  rescncf  12774  limcresi  12841
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