Theorem nfnf1 1523

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 1437	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2		nfa1 1521	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 → ∀𝑥𝜑)
3	1, 2	nfxfr 1450	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1329  Ⅎwnf 1436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  nfimd  1564  nfnt  1634  nfald  1733  equs5or  1802  sbcomxyyz  1945  nfsb4t  1989  nfnfc1  2284  sbcnestgf  3051  dfnfc2  3754  bdsepnft  13085  setindft  13163  strcollnft  13182