Theorem 19.9hOLD 1781

Description: Obsolete proof of 19.9h 1780 as of 5-Jan-2018. (Contributed by FL, 24-Mar-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.9h.1	⊢ (φ → ∀xφ)

Assertion

Ref	Expression
19.9hOLD	⊢ (∃xφ ↔ φ)

Proof of Theorem 19.9hOLD

Step	Hyp	Ref	Expression
1		19.9ht 1778	. . 3 ⊢ (∀x(φ → ∀xφ) → (∃xφ → φ))
2		19.9h.1	. . 3 ⊢ (φ → ∀xφ)
3	1, 2	mpg 1548	. 2 ⊢ (∃xφ → φ)
4		19.8a 1756	. 2 ⊢ (φ → ∃xφ)
5	3, 4	impbii 180	1 ⊢ (∃xφ ↔ φ)

Syntax hints:   → wi 4   ↔ wb 176  ∀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-11 1746

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

This theorem is referenced by: (None)