Theorem hbia1 1417

Description: Lemma 23 of [Monk2] p. 114. (Contributed by NM, 29-May-2008.)

Assertion

Ref	Expression
hbia1	⊢ ((∀xφ → ∀xψ) → ∀x(∀xφ → ∀xψ))

Proof of Theorem hbia1

Step	Hyp	Ref	Expression
1		hba1 1406	. 2 ⊢ (∀xφ → ∀x∀xφ)
2		hba1 1406	. 2 ⊢ (∀xψ → ∀x∀xψ)
3	1, 2	hbim 1410	1 ⊢ ((∀xφ → ∀xψ) → ∀x(∀xφ → ∀xψ))

Syntax hints:   → wi 4  ∀wal 1221

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1309  ax-gen 1311  ax-4 1373  ax-ial 1400  ax-i5r 1401

This theorem is referenced by: (None)