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Theorem exlimd 1574
 Description: Deduction from Theorem 19.9 of [Margaris] p. 89. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 18-Jun-2018.)
Hypotheses
Ref Expression
exlimd.1 𝑥𝜑
exlimd.2 𝑥𝜒
exlimd.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimd (𝜑 → (∃𝑥𝜓𝜒))

Proof of Theorem exlimd
StepHypRef Expression
1 exlimd.1 . . 3 𝑥𝜑
21nfri 1496 . 2 (𝜑 → ∀𝑥𝜑)
3 exlimd.2 . . 3 𝑥𝜒
43nfri 1496 . 2 (𝜒 → ∀𝑥𝜒)
5 exlimd.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimdh 1573 1 (𝜑 → (∃𝑥𝜓𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4  Ⅎwnf 1437  ∃wex 1469 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1424  ax-gen 1426  ax-ie2 1471  ax-4 1487 This theorem depends on definitions:  df-bi 116  df-nf 1438 This theorem is referenced by:  exlimdd  1849  ceqsalg  2737  copsex2t  4200  alxfr  4415  mosubopt  4644  ovmpodf  5942  ovi3  5947  fsum2dlemstep  11308  fprod2dlemstep  11496  bj-exlimmp  13289
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