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

Theorem exlimdOLD 2259
Description: Obsolete proof of exlimd 2125 as of 6-Oct-2021. (Contributed by NM, 23-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 12-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
exlimdOLD.1 𝑥𝜑
exlimdOLD.2 𝑥𝜒
exlimdOLD.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exlimdOLD (𝜑 → (∃𝑥𝜓𝜒))

Proof of Theorem exlimdOLD
StepHypRef Expression
1 exlimdOLD.1 . . 3 𝑥𝜑
2 exlimdOLD.3 . . 3 (𝜑 → (𝜓𝜒))
31, 2eximdOLD 2233 . 2 (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
4 exlimdOLD.2 . . 3 𝑥𝜒
5419.9OLD 2241 . 2 (∃𝑥𝜒𝜒)
63, 5syl6ib 241 1 (𝜑 → (∃𝑥𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1744  wnfOLD 1749
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745  df-nfOLD 1761
This theorem is referenced by:  exlimdhOLD  2260
  Copyright terms: Public domain W3C validator