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Theorem exlimddv 1775
Description: Existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 15-Jun-2016.)
Hypotheses
Ref Expression
exlimddv.1 (φxψ)
exlimddv.2 ((φ ψ) → χ)
Assertion
Ref Expression
exlimddv (φχ)
Distinct variable groups:   χ,x   φ,x
Allowed substitution hint:   ψ(x)

Proof of Theorem exlimddv
StepHypRef Expression
1 exlimddv.1 . 2 (φxψ)
2 exlimddv.2 . . . 4 ((φ ψ) → χ)
32ex 108 . . 3 (φ → (ψχ))
43exlimdv 1697 . 2 (φ → (xψχ))
51, 4mpd 13 1 (φχ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-17 1416
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  fvmptdv2  5203  tfrlemi14d  5888  tfrexlem  5889  erref  6062  xpdom2  6241  genpml  6500  genpmu  6501  ltexprlemm  6572  ltexprlemfl  6581  ltexprlemfu  6583  nn1suc  7674
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