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Theorem bj-exlimh 32933
Description: Closed form of close to exlimih 2312. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-exlimh (∀𝑥(𝜑𝜓) → ((∃𝑥𝜓𝜒) → (∃𝑥𝜑𝜒)))

Proof of Theorem bj-exlimh
StepHypRef Expression
1 exim 1908 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))
21imim1d 82 1 (∀𝑥(𝜑𝜓) → ((∃𝑥𝜓𝜒) → (∃𝑥𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1628  wex 1851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by:  bj-exlimh2  32934
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