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Theorem exlimdd 1889
 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 (φxψ)
exlimdd.4 ((φ ψ) → χ)
Assertion
Ref Expression
exlimdd (φχ)

Proof of Theorem exlimdd
StepHypRef Expression
1 exlimdd.3 . 2 (φxψ)
2 exlimdd.1 . . 3 xφ
3 exlimdd.2 . . 3 xχ
4 exlimdd.4 . . . 4 ((φ ψ) → χ)
54ex 423 . . 3 (φ → (ψχ))
62, 3, 5exlimd 1806 . 2 (φ → (xψχ))
71, 6mpd 14 1 (φχ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∃wex 1541  Ⅎwnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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