Theorem nfnf1 1590

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 1507	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2		nfa1 1587	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 → ∀𝑥𝜑)
3	1, 2	nfxfr 1520	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1393  Ⅎwnf 1506

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-gen 1495  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-nf 1507

This theorem is referenced by:  nfimd  1631  nfnt  1702  nfald  1806  equs5or  1876  sbcomxyyz  2023  nfsb4t  2065  nfnfc1  2375  nfabdw  2391  sbcnestgf  3176  dfnfc2  3905  bdsepnft  16208  setindft  16286  strcollnft  16305