Theorem nfnf1 1476

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 1390	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2		nfa1 1474	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 → ∀𝑥𝜑)
3	1, 2	nfxfr 1403	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1282  Ⅎwnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  nfimd  1517  nfnt  1586  nfald  1683  equs5or  1751  sbcomxyyz  1887  nfsb4t  1931  nfnfc1  2222  sbcnestgf  2953  dfnfc2  3619  bdsepnft  10678  setindft  10760  strcollnft  10779