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Theorem bj-alexim 32589
Description: Closed form of aleximi 1758 (with a shorter proof, so aleximi 1758 could be deduced from it -- exim 1760 would have to be proved first, but its proof is shorter (currently almost a subproof of aleximi 1758)). (Contributed by BJ, 8-Nov-2021.)
Assertion
Ref Expression
bj-alexim (∀𝑥(𝜑 → (𝜓𝜒)) → (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)))

Proof of Theorem bj-alexim
StepHypRef Expression
1 alim 1737 . 2 (∀𝑥(𝜑 → (𝜓𝜒)) → (∀𝑥𝜑 → ∀𝑥(𝜓𝜒)))
2 exim 1760 . 2 (∀𝑥(𝜓𝜒) → (∃𝑥𝜓 → ∃𝑥𝜒))
31, 2syl6 35 1 (∀𝑥(𝜑 → (𝜓𝜒)) → (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1480  wex 1703
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736
This theorem depends on definitions:  df-bi 197  df-ex 1704
This theorem is referenced by:  bj-exalim  32595
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