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Theorem bj-alexim 34034
Description: Closed form of aleximi 1833. Note: this proof is shorter, so aleximi 1833 could be deduced from it (exim 1835 would have to be proved first, see bj-eximALT 34048 but its proof is shorter (currently almost a subproof of aleximi 1833)). (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 1812 . 2 (∀𝑥(𝜑 → (𝜓𝜒)) → (∀𝑥𝜑 → ∀𝑥(𝜓𝜒)))
2 exim 1835 . 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 1536  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by:  bj-exalim  34039  bj-cbveximt  34047
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