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Theorem exlimd 1529
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 1453 . 2 (𝜑 → ∀𝑥𝜑)
3 exlimd.2 . . 3 𝑥𝜒
43nfri 1453 . 2 (𝜒 → ∀𝑥𝜒)
5 exlimd.3 . 2 (𝜑 → (𝜓𝜒))
62, 4, 5exlimdh 1528 1 (𝜑 → (∃𝑥𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1390  wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1377  ax-gen 1379  ax-ie2 1424  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  exlimdd  1794  ceqsalg  2628  copsex2t  4008  alxfr  4219  mosubopt  4431  ovmpt2df  5663  ovi3  5668  bj-exlimmp  10731
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