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Theorem bj-nfdiOLD 31860
 Description: Obsolete proof temporarily kept here in view of the change of df-nf 1699 to nf2 2090. (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 1988 . . 3 (𝜑 → ∃𝑥𝜑)
2 bj-nfdiOLD.nf . . . 4 (𝜑 → Ⅎ𝑥𝜑)
3 nf2 2090 . . . 4 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
42, 3sylib 206 . . 3 (𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
51, 4mpd 15 . 2 (𝜑 → ∀𝑥𝜑)
65nfi 1705 1 𝑥𝜑
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1472  ∃wex 1694  Ⅎwnf 1698 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-12 1983 This theorem depends on definitions:  df-bi 195  df-ex 1695  df-nf 1699 This theorem is referenced by: (None)
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