Theorem nfnf1 1592

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 1509	. 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2		nfa1 1589	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 → ∀𝑥𝜑)
3	1, 2	nfxfr 1522	1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑

Syntax hints:   → wi 4  ∀wal 1395  Ⅎwnf 1508

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 1495  ax-gen 1497  ax-ial 1582

This theorem depends on definitions:  df-bi 117  df-nf 1509

This theorem is referenced by:  nfimd  1633  nfnt  1704  nfald  1808  equs5or  1878  sbcomxyyz  2025  nfsb4t  2067  nfnfc1  2377  nfabdw  2393  sbcnestgf  3179  dfnfc2  3911  bdsepnft  16482  setindft  16560  strcollnft  16579