Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-sylget2 Structured version   Visualization version   GIF version

Theorem bj-sylget2 34068
Description: Uncurried (imported) form of bj-sylget 34067. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sylget2 ((∀𝑥(𝜑𝜓) ∧ (∃𝑥𝜓𝜒)) → (∃𝑥𝜑𝜒))

Proof of Theorem bj-sylget2
StepHypRef Expression
1 bj-sylget 34067 . 2 (∀𝑥(𝜑𝜓) → ((∃𝑥𝜓𝜒) → (∃𝑥𝜑𝜒)))
21imp 410 1 ((∀𝑥(𝜑𝜓) ∧ (∃𝑥𝜓𝜒)) → (∃𝑥𝜑𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wal 1536  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator