Theorem nfa1-o 33218

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 33200	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2	1	nf5i 2011	1 ⊢ Ⅎ𝑥∀𝑥𝜑

Syntax hints:  ∀wal 1473  Ⅎwnf 1699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-10 2006  ax-c5 33186  ax-c4 33187  ax-c7 33188

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701

This theorem is referenced by:  axc11n-16  33241  ax12eq  33244  ax12el  33245  ax12v2-o  33252