Theorem nfa1-o 39414

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 39396	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2	1	nf5i 2157	1 ⊢ Ⅎ𝑥∀𝑥𝜑

Syntax hints:  ∀wal 1545  Ⅎwnf 1790

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-10 2152  ax-c5 39382  ax-c4 39383  ax-c7 39384

This theorem depends on definitions:  df-bi 208  df-ex 1787  df-nf 1791

This theorem is referenced by:  axc11n-16  39437  ax12eq  39440  ax12el  39441  ax12v2-o  39448