Theorem nfa1-o 39940

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 39922	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2	1	nf5i 2183	1 ⊢ Ⅎ𝑥∀𝑥𝜑

This proof depends on syntax axioms:  ∀wal 1568  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-10 2178  ax-c5 39908  ax-c4 39909  ax-c7 39910

This proof depends on definitions:  df-bi 210  df-ex 1813  df-nf 1817

This theorem is used by:  axc11n-16  39963  ax12eq  39966  ax12el  39967  ax12v2-o  39974