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Theorem 2eximdv 1762
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 3-Aug-1995.)
Hypothesis
Ref Expression
2alimdv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
2eximdv (𝜑 → (∃𝑥𝑦𝜓 → ∃𝑥𝑦𝜒))
Distinct variable groups:   𝜑,𝑥   𝜑,𝑦
Allowed substitution hints:   𝜓(𝑥,𝑦)   𝜒(𝑥,𝑦)

Proof of Theorem 2eximdv
StepHypRef Expression
1 2alimdv.1 . . 3 (𝜑 → (𝜓𝜒))
21eximdv 1760 . 2 (𝜑 → (∃𝑦𝜓 → ∃𝑦𝜒))
32eximdv 1760 1 (𝜑 → (∃𝑥𝑦𝜓 → ∃𝑥𝑦𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1381
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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  cgsex2g  2590  cgsex4g  2591  spc2egv  2642  spc3egv  2644  relop  4486  elres  4646  opabbrex  5549  th3q  6211  addnnnq0  6547  mulnnnq0  6548  prmuloc  6664  addsrpr  6830  mulsrpr  6831
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