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Theorem exlimdd 1752
 Description: Existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
exlimdd.1 𝑥𝜑
exlimdd.2 𝑥𝜒
exlimdd.3 (𝜑 → ∃𝑥𝜓)
exlimdd.4 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
exlimdd (𝜑𝜒)

Proof of Theorem exlimdd
StepHypRef Expression
1 exlimdd.3 . 2 (𝜑 → ∃𝑥𝜓)
2 exlimdd.1 . . 3 𝑥𝜑
3 exlimdd.2 . . 3 𝑥𝜒
4 exlimdd.4 . . . 4 ((𝜑𝜓) → 𝜒)
54ex 108 . . 3 (𝜑 → (𝜓𝜒))
62, 3, 5exlimd 1488 . 2 (𝜑 → (∃𝑥𝜓𝜒))
71, 6mpd 13 1 (𝜑𝜒)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97  Ⅎwnf 1349  ∃wex 1381 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-4 1400 This theorem depends on definitions:  df-bi 110  df-nf 1350 This theorem is referenced by:  fvmptdf  5258  ovmpt2df  5632  ltexprlemm  6698
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