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

Theorem exanOLD 1854
Description: Obsolete proof of exan 1853 as of 19-Jun-2023. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) Reduce axiom dependencies. (Revised by BJ, 7-Jul-2021.) (Proof shortened by Wolf Lammen, 6-Nov-2022.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
exanOLD.1 (∃𝑥𝜑𝜓)
Assertion
Ref Expression
exanOLD 𝑥(𝜑𝜓)

Proof of Theorem exanOLD
StepHypRef Expression
1 exanOLD.1 . . 3 (∃𝑥𝜑𝜓)
21simpli 484 . 2 𝑥𝜑
31simpri 486 . . 3 𝜓
43jctr 525 . 2 (𝜑 → (𝜑𝜓))
52, 4eximii 1828 1 𝑥(𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wa 396  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator