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Theorem exlimddOLD 2217
Description: Obsolete version of exlimdd 2216 as of 3-Sep-2023. (Contributed by Mario Carneiro, 9-Feb-2017.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
exlimdd.1 𝑥𝜑
exlimdd.2 𝑥𝜒
exlimdd.3 (𝜑 → ∃𝑥𝜓)
exlimdd.4 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
exlimddOLD (𝜑𝜒)

Proof of Theorem exlimddOLD
StepHypRef Expression
1 exlimdd.3 . 2 (𝜑 → ∃𝑥𝜓)
2 exlimdd.1 . . 3 𝑥𝜑
3 exlimdd.2 . . 3 𝑥𝜒
4 exlimdd.4 . . . 4 ((𝜑𝜓) → 𝜒)
54ex 415 . . 3 (𝜑 → (𝜓𝜒))
62, 3, 5exlimd 2214 . 2 (𝜑 → (∃𝑥𝜓𝜒))
71, 6mpd 15 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  wex 1776  wnf 1780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-12 2173
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-nf 1781
This theorem is referenced by: (None)
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