Theorem nfa1-o 34519

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 34501	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2	1	nf5i 2064	1 ⊢ Ⅎ𝑥∀𝑥𝜑

Syntax hints:  ∀wal 1521  Ⅎwnf 1748

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-10 2059  ax-c5 34487  ax-c4 34488  ax-c7 34489

This theorem depends on definitions:  df-bi 197  df-ex 1745  df-nf 1750

This theorem is referenced by:  axc11n-16  34542  ax12eq  34545  ax12el  34546  ax12v2-o  34553