Theorem hbnOLD 1777

Description: Obsolete proof of hbn 1776 as of 16-Dec-2017. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
hbn.1	⊢ (φ → ∀xφ)

Assertion

Ref	Expression
hbnOLD	⊢ (¬ φ → ∀x ¬ φ)

Proof of Theorem hbnOLD

Step	Hyp	Ref	Expression
1		sp 1747	. . 3 ⊢ (∀xφ → φ)
2	1	con3i 127	. 2 ⊢ (¬ φ → ¬ ∀xφ)
3		hbn1 1730	. . 3 ⊢ (¬ ∀xφ → ∀x ¬ ∀xφ)
4		hbn.1	. . . 4 ⊢ (φ → ∀xφ)
5	4	con3i 127	. . 3 ⊢ (¬ ∀xφ → ¬ φ)
6	3, 5	alrimih 1565	. 2 ⊢ (¬ ∀xφ → ∀x ¬ φ)
7	2, 6	syl 15	1 ⊢ (¬ φ → ∀x ¬ φ)

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)