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

Theorem bj-alrimhi 32243
Description: An inference associated with sylgt 1746 and bj-exlimh 32241. (Contributed by BJ, 12-May-2019.)
Hypothesis
Ref Expression
bj-alrimhi.1 (𝜑𝜓)
Assertion
Ref Expression
bj-alrimhi (Ⅎ𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-alrimhi
StepHypRef Expression
1 df-nf 1707 . . 3 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
21biimpi 206 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
3 bj-alrimhi.1 . . 3 (𝜑𝜓)
43alimi 1736 . 2 (∀𝑥𝜑 → ∀𝑥𝜓)
52, 4syl6 35 1 (Ⅎ𝑥𝜑 → (∃𝑥𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wex 1701  wnf 1705
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-nf 1707
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator