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Theorem exlimdvv 1793
Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 31-Jul-1995.)
Hypothesis
Ref Expression
exlimdvv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimdvv (𝜑 → (∃𝑥𝑦𝜓𝜒))
Distinct variable groups:   𝜒,𝑥   𝜑,𝑥   𝜒,𝑦   𝜑,𝑦
Allowed substitution hints:   𝜓(𝑥,𝑦)

Proof of Theorem exlimdvv
StepHypRef Expression
1 exlimdvv.1 . . 3 (𝜑 → (𝜓𝜒))
21exlimdv 1716 . 2 (𝜑 → (∃𝑦𝜓𝜒))
32exlimdv 1716 1 (𝜑 → (∃𝑥𝑦𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-5 1352  ax-gen 1354  ax-ie2 1399  ax-17 1435
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  euotd  4019  funopg  4962  th3qlem1  6239  fundmen  6317  addnq0mo  6603  mulnq0mo  6604  genprndl  6677  genprndu  6678  genpdisj  6679  mullocpr  6727  addsrmo  6886  mulsrmo  6887
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