Theorem 19.12OLD 1848

Description: Obsolete proof of 19.12 1847 as of 3-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.12OLD	⊢ (∃x∀yφ → ∀y∃xφ)

Proof of Theorem 19.12OLD

Step	Hyp	Ref	Expression
1		hba1 1786	. . 3 ⊢ (∀yφ → ∀y∀yφ)
2	1	hbex 1841	. 2 ⊢ (∃x∀yφ → ∀y∃x∀yφ)
3		sp 1747	. . 3 ⊢ (∀yφ → φ)
4	3	eximi 1576	. 2 ⊢ (∃x∀yφ → ∃xφ)
5	2, 4	alrimih 1565	1 ⊢ (∃x∀yφ → ∀y∃xφ)

Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1541

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-7 1734  ax-11 1746

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

This theorem is referenced by: (None)