Theorem hba1OLD 1787

Description: Obsolete proof of hba1 1786 as of 15-Dec-2017. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
hba1OLD	⊢ (∀xφ → ∀x∀xφ)

Proof of Theorem hba1OLD

Step	Hyp	Ref	Expression
1		sp 1747	. . 3 ⊢ (∀x ¬ ∀xφ → ¬ ∀xφ)
2	1	con2i 112	. 2 ⊢ (∀xφ → ¬ ∀x ¬ ∀xφ)
3		hbn1 1730	. 2 ⊢ (¬ ∀x ¬ ∀xφ → ∀x ¬ ∀x ¬ ∀xφ)
4		hbn1 1730	. . . 4 ⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)
5	4	con1i 121	. . 3 ⊢ (¬ ∀x ¬ ∀xφ → ∀xφ)
6	5	alimi 1559	. 2 ⊢ (∀x ¬ ∀x ¬ ∀xφ → ∀x∀xφ)
7	2, 3, 6	3syl 18	1 ⊢ (∀xφ → ∀x∀xφ)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)