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

Theorem bj-nfdiOLD 32019
Description: Obsolete proof temporarily kept here in view of the change of nf5 2102 to df-nf 1701. (Contributed by NM, 8-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
bj-nfdiOLD.nf (𝜑 → Ⅎ𝑥𝜑)
Assertion
Ref Expression
bj-nfdiOLD 𝑥𝜑

Proof of Theorem bj-nfdiOLD
StepHypRef Expression
1 19.8a 2039 . . 3 (𝜑 → ∃𝑥𝜑)
2 bj-nfdiOLD.nf . . . 4 (𝜑 → Ⅎ𝑥𝜑)
3 df-nf 1701 . . . 4 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
42, 3sylib 207 . . 3 (𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
51, 4mpd 15 . 2 (𝜑 → ∀𝑥𝜑)
65nf5i 2011 1 𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1473  wex 1695  wnf 1699
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  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator