Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfdvOLD Structured version   Visualization version   GIF version

Theorem nfdvOLD 1860
 Description: Obsolete proof of nf5dv 2012 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfdvOLD.1 (𝜑 → (𝜓 → ∀𝑥𝜓))
Assertion
Ref Expression
nfdvOLD (𝜑 → Ⅎ𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem nfdvOLD
StepHypRef Expression
1 nfdvOLD.1 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
21alrimiv 1842 . 2 (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))
3 df-nfOLD 1712 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
42, 3sylibr 223 1 (𝜑 → Ⅎ𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473  ℲwnfOLD 1700 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827 This theorem depends on definitions:  df-bi 196  df-nfOLD 1712 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator