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

Theorem exlimiOLD 2257
Description: Obsolete proof of exlimi 2124 as of 6-Oct-2021. (Contributed by NM, 10-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exlimiOLD.1 𝑥𝜓
exlimiOLD.2 (𝜑𝜓)
Assertion
Ref Expression
exlimiOLD (∃𝑥𝜑𝜓)

Proof of Theorem exlimiOLD
StepHypRef Expression
1 exlimiOLD.1 . . 3 𝑥𝜓
2119.23OLD 2255 . 2 (∀𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
3 exlimiOLD.2 . 2 (𝜑𝜓)
42, 3mpgbi 1765 1 (∃𝑥𝜑𝜓)
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-or 384  df-ex 1745  df-nf 1750  df-nfOLD 1761
This theorem is referenced by:  exlimihOLD  2258
  Copyright terms: Public domain W3C validator