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Theorem exlimd 1557
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 1480 . 2 (𝜑 → ∀𝑥𝜑)
3 exlimd.2 . . 3 𝑥𝜒
43nfri 1480 . 2 (𝜒 → ∀𝑥𝜒)
5 exlimd.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimdh 1556 1 (𝜑 → (∃𝑥𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1417  wex 1449
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-5 1404  ax-gen 1406  ax-ie2 1451  ax-4 1468
This theorem depends on definitions:  df-bi 116  df-nf 1418
This theorem is referenced by:  exlimdd  1824  ceqsalg  2683  copsex2t  4125  alxfr  4340  mosubopt  4562  ovmpodf  5854  ovi3  5859  fsum2dlemstep  11089  bj-exlimmp  12660
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