Theorem exiftruOLD 1658

Description: Obsolete proof of exiftru 1657 as of 9-Dec-2017. (Contributed by Wolf Lammen, 12-Nov-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
exiftruOLD.1	⊢ φ

Assertion

Ref	Expression
exiftruOLD	⊢ ∃xφ

Proof of Theorem exiftruOLD

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		a9ev 1656	. . . 4 ⊢ ∃x x = y
2	1	a1i 10	. . 3 ⊢ (∀x x = y → ∃x x = y)
3	2	19.35ri 1602	. 2 ⊢ ∃x(x = y → x = y)
4		exiftruOLD.1	. . . 4 ⊢ φ
5		id 19	. . . 4 ⊢ (x = y → x = y)
6	4, 5	2th 230	. . 3 ⊢ (φ ↔ (x = y → x = y))
7	6	exbii 1582	. 2 ⊢ (∃xφ ↔ ∃x(x = y → x = y))
8	3, 7	mpbir 200	1 ⊢ ∃xφ

This proof depends on syntax axioms:   → wi 4  ∀wal 1540  ∃wex 1541

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-9 1654

This proof depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is used by: (None)