MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exlimimddOLD Structured version   Visualization version   GIF version

Theorem exlimimddOLD 2224
Description: Obsolete version of exlimimdd 2221 as of 3-Sep-2023. (Contributed by ML, 17-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exlimdd.1 𝑥𝜑
exlimdd.2 𝑥𝜒
exlimdd.3 (𝜑 → ∃𝑥𝜓)
exlimimddOLD.4 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimimddOLD (𝜑𝜒)

Proof of Theorem exlimimddOLD
StepHypRef Expression
1 exlimdd.1 . 2 𝑥𝜑
2 exlimdd.2 . 2 𝑥𝜒
3 exlimdd.3 . 2 (𝜑 → ∃𝑥𝜓)
4 exlimimddOLD.4 . . 3 (𝜑 → (𝜓𝜒))
54imp 410 . 2 ((𝜑𝜓) → 𝜒)
61, 2, 3, 5exlimdd 2222 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1781  wnf 1785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator