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Theorem bj-aleximiALT 34032
Description: Alternate proof of aleximi 1833 from exim 1835, which is sometimes used as an axiom in instuitionistic modal logic. (Contributed by BJ, 9-Dec-2023.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
bj-aleximiALT.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
bj-aleximiALT (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Proof of Theorem bj-aleximiALT
StepHypRef Expression
1 bj-aleximiALT.1 . . 3 (𝜑 → (𝜓𝜒))
21alimi 1813 . 2 (∀𝑥𝜑 → ∀𝑥(𝜓𝜒))
3 bj-eximALT 34031 . 2 (∀𝑥(𝜓𝜒) → (∃𝑥𝜓 → ∃𝑥𝜒))
42, 3syl 17 1 (∀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: (None)
  Copyright terms: Public domain W3C validator