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

Theorem bj-sylget 34039
Description: Dual statement of sylgt 1823. Closed form of bj-sylge 34042. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sylget (∀𝑥(𝜒𝜑) → ((∃𝑥𝜑𝜓) → (∃𝑥𝜒𝜓)))

Proof of Theorem bj-sylget
StepHypRef Expression
1 exim 1835 . 2 (∀𝑥(𝜒𝜑) → (∃𝑥𝜒 → ∃𝑥𝜑))
21imim1d 82 1 (∀𝑥(𝜒𝜑) → ((∃𝑥𝜑𝜓) → (∃𝑥𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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-ex 1782
This theorem is referenced by:  bj-sylget2  34040  bj-exlimg  34041
  Copyright terms: Public domain W3C validator