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	⊢ Ⅎ𝑥𝜑

Proof of Theorem bj-nfdiOLD

Step	Hyp	Ref	Expression
1		19.8a 2039	. . 3 ⊢ (𝜑 → ∃𝑥𝜑)
2		bj-nfdiOLD.nf	. . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜑)
3		df-nf 1701	. . . 4 ⊢ (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
4	2, 3	sylib 207	. . 3 ⊢ (𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑))
5	1, 4	mpd 15	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
6	5	nf5i 2011	1 ⊢ Ⅎ𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1473  ∃wex 1695  Ⅎwnf 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)