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Theorem bj-sylget 35075
Description: Dual statement of sylgt 1824. Closed form of bj-sylge 35078. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sylget (∀𝑥(𝜒𝜑) → ((∃𝑥𝜑𝜓) → (∃𝑥𝜒𝜓)))

Proof of Theorem bj-sylget
StepHypRef Expression
1 exim 1836 . 2 (∀𝑥(𝜒𝜑) → (∃𝑥𝜒 → ∃𝑥𝜑))
21imim1d 82 1 (∀𝑥(𝜒𝜑) → ((∃𝑥𝜑𝜓) → (∃𝑥𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1539  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 206  df-ex 1782
This theorem is referenced by:  bj-sylget2  35076  bj-exlimg  35077
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