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Theorem exlimdd 1730
 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 108 . . 3 (φ → (ψχ))
62, 3, 5exlimd 1466 . 2 (φ → (xψχ))
71, 6mpd 13 1 (φχ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97  Ⅎwnf 1325  ∃wex 1358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia3 101  ax-5 1312  ax-gen 1314  ax-ie2 1360  ax-4 1377 This theorem depends on definitions:  df-bi 110  df-nf 1326 This theorem is referenced by:  fvmptdf  5179  ovmpt2df  5551  ltexprlemm  6431
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