Theorem nfa1-o 2166

Description: x is not free in ∀xφ. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nfa1-o	⊢ Ⅎx∀xφ

Proof of Theorem nfa1-o

Step	Hyp	Ref	Expression
1		hba1-o 2149	. 2 ⊢ (∀xφ → ∀x∀xφ)
2	1	nfi 1551	1 ⊢ Ⅎx∀xφ

Syntax hints:  ∀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-4 2135  ax-5o 2136  ax-6o 2137

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

This theorem is referenced by:  ax10-16  2190  ax11eq  2193  ax11el  2194  ax11v2-o  2201