Theorem nfnf1 1488

Description: 𝑥 is not free in Ⅎ𝑥𝜑. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfnf1	⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Proof of Theorem nfnf1

Step	Hyp	Ref	Expression
1		df-nf 1402	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2		nfa1 1486	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 → ∀𝑥𝜑)
3	1, 2	nfxfr 1415	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1294  Ⅎwnf 1401

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ial 1479

This theorem depends on definitions:  df-bi 116  df-nf 1402

This theorem is referenced by:  nfimd  1529  nfnt  1598  nfald  1697  equs5or  1765  sbcomxyyz  1901  nfsb4t  1945  nfnfc1  2238  sbcnestgf  2993  dfnfc2  3693  bdsepnft  12486  setindft  12568  strcollnft  12587