Theorem nfnf1 1790

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 1545	. 2 ⊢ (Ⅎxφ ↔ ∀x(φ → ∀xφ))
2		nfa1 1788	. 2 ⊢ Ⅎx∀x(φ → ∀xφ)
3	1, 2	nfxfr 1570	1 ⊢ ℲxℲxφ

Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  nfnd  1791  nfndOLD  1792  nfimd  1808  19.23tOLD  1819  nfald  1852  nfaldOLD  1853  spimt  1974  spimed  1977  nfnfc1  2493  sbcnestgf  3184  dfnfc2  3910