Theorem nfnf1OLD 2306

Description: Obsolete proof of nfnf1 2180 as of 12-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nfnf1OLD	⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Proof of Theorem nfnf1OLD

Step	Hyp	Ref	Expression
1		nf5 2263	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2		nfa1 2177	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 → ∀𝑥𝜑)
3	1, 2	nfxfr 1928	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1630  Ⅎwnf 1857

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196

This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1854  df-nf 1859

This theorem is referenced by: (None)