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Theorem 2eximdv 1855
 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 1853 . 2 (𝜑 → (∃𝑦𝜓 → ∃𝑦𝜒))
32eximdv 1853 1 (𝜑 → (∃𝑥𝑦𝜓 → ∃𝑥𝑦𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4  ∃wex 1469 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 This theorem is referenced by:  cgsex2g  2726  cgsex4g  2727  spc2egv  2780  spc3egv  2782  relop  4700  elres  4866  opabbrex  5826  th3q  6545  addnnnq0  7308  mulnnnq0  7309  prmuloc  7425  addsrpr  7604  mulsrpr  7605
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