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Theorem bj-sylge 34070
Description: Dual statement of sylg 1824 (the final "e" in the label stands for "existential (version of sylg 1824)". Variant of exlimih 2293. (Contributed by BJ, 25-Dec-2023.)
Hypotheses
Ref Expression
bj-sylge.nf (∃𝑥𝜑𝜓)
bj-sylge.maj (𝜒𝜑)
Assertion
Ref Expression
bj-sylge (∃𝑥𝜒𝜓)

Proof of Theorem bj-sylge
StepHypRef Expression
1 bj-sylge.maj . . 3 (𝜒𝜑)
21eximi 1836 . 2 (∃𝑥𝜒 → ∃𝑥𝜑)
3 bj-sylge.nf . 2 (∃𝑥𝜑𝜓)
42, 3syl 17 1 (∃𝑥𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  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-cbvexiw  34117
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