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Theorem 2eximdv 1838
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 1836 . 2 (𝜑 → (∃𝑦𝜓 → ∃𝑦𝜒))
32eximdv 1836 1 (𝜑 → (∃𝑥𝑦𝜓 → ∃𝑥𝑦𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1453
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  cgsex2g  2696  cgsex4g  2697  spc2egv  2749  spc3egv  2751  relop  4659  elres  4825  opabbrex  5783  th3q  6502  addnnnq0  7225  mulnnnq0  7226  prmuloc  7342  addsrpr  7521  mulsrpr  7522
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