Theorem wl-nfalv 32491

Description: If 𝑥 is not present in 𝜑, it is not free in ∀𝑦𝜑. (Contributed by Wolf Lammen, 11-Jan-2020.)

Assertion

Ref	Expression
wl-nfalv	⊢ Ⅎ𝑥∀𝑦𝜑

Distinct variable group:   𝜑,𝑥

Allowed substitution hint:   𝜑(𝑦)

Proof of Theorem wl-nfalv

Step	Hyp	Ref	Expression
1		ax-5 1827	. . 3 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	hbal 2023	. 2 ⊢ (∀𝑦𝜑 → ∀𝑥∀𝑦𝜑)
3	2	nf5i 2011	1 ⊢ Ⅎ𝑥∀𝑦𝜑

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-5 1827  ax-10 2006  ax-11 2021

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

This theorem is referenced by: (None)