Theorem nfa1-o 38897

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 38879	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2	1	nf5i 2144	1 ⊢ Ⅎ𝑥∀𝑥𝜑

Syntax hints:  ∀wal 1535  Ⅎwnf 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-10 2139  ax-c5 38865  ax-c4 38866  ax-c7 38867

This theorem depends on definitions:  df-bi 207  df-ex 1777  df-nf 1781

This theorem is referenced by:  axc11n-16  38920  ax12eq  38923  ax12el  38924  ax12v2-o  38931