Theorem hbaltg 33054

Description: A more general and closed form of hbal 2174. (Contributed by Scott Fenton, 13-Dec-2010.)

Assertion

Ref	Expression
hbaltg	⊢ (∀𝑥(𝜑 → ∀𝑦𝜓) → (∀𝑥𝜑 → ∀𝑦∀𝑥𝜓))

Proof of Theorem hbaltg

Step	Hyp	Ref	Expression
1		alim 1811	. 2 ⊢ (∀𝑥(𝜑 → ∀𝑦𝜓) → (∀𝑥𝜑 → ∀𝑥∀𝑦𝜓))
2		ax-11 2161	. 2 ⊢ (∀𝑥∀𝑦𝜓 → ∀𝑦∀𝑥𝜓)
3	1, 2	syl6 35	1 ⊢ (∀𝑥(𝜑 → ∀𝑦𝜓) → (∀𝑥𝜑 → ∀𝑦∀𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1810  ax-11 2161

This theorem is referenced by: (None)