Theorem 19.9hOLD 2194

Description: Obsolete proof of 19.9h 2106 as of 6-Oct-2021. (Contributed by FL, 24-Mar-2007.) (Proof shortened by Wolf Lammen, 5-Jan-2018.) (Proof shortened by Wolf Lammen, 14-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.9hOLD.1	⊢ (𝜑 → ∀𝑥𝜑)

Assertion

Ref	Expression
19.9hOLD	⊢ (∃𝑥𝜑 ↔ 𝜑)

Proof of Theorem 19.9hOLD

Step	Hyp	Ref	Expression
1		19.9hOLD.1	. . 3 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	nfiOLD 1725	. 2 ⊢ Ⅎ𝑥𝜑
3	2	19.9OLD 2193	1 ⊢ (∃𝑥𝜑 ↔ 𝜑)

Syntax hints:   → wi 4   ↔ wb 195  ∀wal 1473  ∃wex 1695

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-nfOLD 1712

This theorem is referenced by: (None)