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Theorem exlimimd 35251
Description: Existential elimination rule of natural deduction. (Contributed by ML, 17-Jul-2020.)
Hypotheses
Ref Expression
exlimimd.1 (𝜑 → ∃𝑥𝜓)
exlimimd.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimimd (𝜑𝜒)
Distinct variable groups:   𝜑,𝑥   𝜒,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem exlimimd
StepHypRef Expression
1 exlimimd.1 . 2 (𝜑 → ∃𝑥𝜓)
2 exlimimd.2 . . 3 (𝜑 → (𝜓𝜒))
32imp 410 . 2 ((𝜑𝜓) → 𝜒)
41, 3exlimddv 1943 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1787
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788
This theorem is referenced by: (None)
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