Theorem hba2 1565

Description: Lemma 24 of [Monk2] p. 114. (Contributed by NM, 29-May-2008.)

Assertion

Ref	Expression
hba2	⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦∀𝑥𝜑)

Proof of Theorem hba2

Step	Hyp	Ref	Expression
1		hba1 1554	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2	1	hbal 1491	1 ⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦∀𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ial 1548

This theorem is referenced by: (None)