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 36006
Description: Dual statement of sylgt 1816. Closed form of bj-sylge 36009. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sylget (∀𝑥(𝜒𝜑) → ((∃𝑥𝜑𝜓) → (∃𝑥𝜒𝜓)))

Proof of Theorem bj-sylget
StepHypRef Expression
1 exim 1828 . 2 (∀𝑥(𝜒𝜑) → (∃𝑥𝜒 → ∃𝑥𝜑))
21imim1d 82 1 (∀𝑥(𝜒𝜑) → ((∃𝑥𝜑𝜓) → (∃𝑥𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wex 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803
This theorem depends on definitions:  df-bi 206  df-ex 1774
This theorem is referenced by:  bj-sylget2  36007  bj-exlimg  36008
  Copyright terms: Public domain W3C validator