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Theorem exlimdh 2295
 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 2148 . 2 𝑥𝜑
3 exlimdh.2 . . 3 (𝜒 → ∀𝑥𝜒)
43nf5i 2148 . 2 𝑥𝜒
5 exlimdh.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimd 2217 1 (𝜑 → (∃𝑥𝜓𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1782 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2143  ax-12 2176 This theorem depends on definitions:  df-bi 210  df-ex 1783  df-nf 1787 This theorem is referenced by:  exlimexi  41596  eexinst01  41598  eexinst11  41599
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