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

Theorem bj-nfdt 32811
Description: Closed form of nf5d 2156 and nf5dh 2066. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfdt (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓)))

Proof of Theorem bj-nfdt
StepHypRef Expression
1 bj-nfdt0 32810 . 2 (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓))
21imim2d 57 1 (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521  wnf 1748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1745  df-nf 1750
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator