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Theorem exlimdh 2328
Description: Deduction form of Theorem 19.9 of [Margaris] p. 89. (Contributed by NM, 28-Jan-1997.)
Hypotheses
Ref Expression
exlimdh.1 (𝜑 → ∀𝑥𝜑)
exlimdh.2 (𝜒 → ∀𝑥𝜒)
exlimdh.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimdh (𝜑 → (∃𝑥𝜓𝜒))

Proof of Theorem exlimdh
StepHypRef Expression
1 exlimdh.1 . . 3 (𝜑 → ∀𝑥𝜑)
21nf5i 2191 . 2 𝑥𝜑
3 exlimdh.2 . . 3 (𝜒 → ∀𝑥𝜒)
43nf5i 2191 . 2 𝑥𝜒
5 exlimdh.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimd 2255 1 (𝜑 → (∃𝑥𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1635  wex 1859
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2069  ax-7 2105  ax-10 2186  ax-12 2215
This theorem depends on definitions:  df-bi 198  df-ex 1860  df-nf 1864
This theorem is referenced by:  exlimexi  39229  eexinst01  39231  eexinst11  39232
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