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Theorem exlimii 35001
Description: Inference associated with exlimi 2210. Inferring a theorem when it is implied by an antecedent which may be true. (Contributed by BJ, 15-Sep-2018.)
Hypotheses
Ref Expression
exlimii.1 𝑥𝜓
exlimii.2 (𝜑𝜓)
exlimii.3 𝑥𝜑
Assertion
Ref Expression
exlimii 𝜓

Proof of Theorem exlimii
StepHypRef Expression
1 exlimii.3 . 2 𝑥𝜑
2 exlimii.1 . . 3 𝑥𝜓
3 exlimii.2 . . 3 (𝜑𝜓)
42, 3exlimi 2210 . 2 (∃𝑥𝜑𝜓)
51, 4ax-mp 5 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1782  wnf 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171
This theorem depends on definitions:  df-bi 206  df-ex 1783  df-nf 1787
This theorem is referenced by:  exlimiieq1  35004  exlimiieq2  35005
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