Theorem 19.3OLD 2190

Description: Obsolete proof of 19.3 2057 as of 6-Oct-2021. (Contributed by NM, 12-Mar-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.3OLD.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
19.3OLD	⊢ (∀𝑥𝜑 ↔ 𝜑)

Proof of Theorem 19.3OLD

Step	Hyp	Ref	Expression
1		sp 2041	. 2 ⊢ (∀𝑥𝜑 → 𝜑)
2		19.3OLD.1	. . 3 ⊢ Ⅎ𝑥𝜑
3	2	nfriOLD 2177	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
4	1, 3	impbii 198	1 ⊢ (∀𝑥𝜑 ↔ 𝜑)

Syntax hints:   ↔ wb 195  ∀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  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712

This theorem is referenced by:  19.27OLD  2222  19.28OLD  2223