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Theorem exlimdh 2134
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 2011 . 2 𝑥𝜑
3 exlimdh.2 . . 3 (𝜒 → ∀𝑥𝜒)
43nf5i 2011 . 2 𝑥𝜒
5 exlimdh.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimd 2074 1 (𝜑 → (∃𝑥𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1473  wex 1695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701
This theorem is referenced by:  exlimexi  37751  eexinst01  37753  eexinst11  37754
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