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Theorem exlimih 2144
Description: Inference associated with 19.23 2078. See exlimiv 1855 for a version with a dv condition requiring fewer axioms. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
Hypotheses
Ref Expression
exlimih.1 (𝜓 → ∀𝑥𝜓)
exlimih.2 (𝜑𝜓)
Assertion
Ref Expression
exlimih (∃𝑥𝜑𝜓)

Proof of Theorem exlimih
StepHypRef Expression
1 exlimih.1 . . 3 (𝜓 → ∀𝑥𝜓)
21nf5i 2021 . 2 𝑥𝜓
3 exlimih.2 . 2 (𝜑𝜓)
42, 3exlimi 2084 1 (∃𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1702  df-nf 1707
This theorem is referenced by: (None)
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