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Theorem exlimimdd 33321
 Description: Existential elimination rule of natural deduction. (Contributed by ML, 17-Jul-2020.)
Hypotheses
Ref Expression
exlimimdd.1 𝑥𝜑
exlimimdd.2 𝑥𝜒
exlimimdd.3 (𝜑 → ∃𝑥𝜓)
exlimimdd.4 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimimdd (𝜑𝜒)

Proof of Theorem exlimimdd
StepHypRef Expression
1 exlimimdd.1 . 2 𝑥𝜑
2 exlimimdd.2 . 2 𝑥𝜒
3 exlimimdd.3 . 2 (𝜑 → ∃𝑥𝜓)
4 exlimimdd.4 . . 3 (𝜑 → (𝜓𝜒))
54imp 444 . 2 ((𝜑𝜓) → 𝜒)
61, 2, 3, 5exlimdd 2126 1 (𝜑𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1744  Ⅎwnf 1748 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745  df-nf 1750 This theorem is referenced by: (None)
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