Theorem 19.9vOLD 1697

Description: Obsolete version of 19.9v 1664 as of 4-Dec-2017. (Contributed by NM, 28-May-1995.) (Revised by NM, 1-Aug-2017.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
19.9vOLD	⊢ (∃xφ ↔ φ)

Distinct variable group:   φ,x

Proof of Theorem 19.9vOLD

Step	Hyp	Ref	Expression
1		df-ex 1542	. 2 ⊢ (∃xφ ↔ ¬ ∀x ¬ φ)
2		19.3v 1665	. . 3 ⊢ (∀x ¬ φ ↔ ¬ φ)
3	2	con2bii 322	. 2 ⊢ (φ ↔ ¬ ∀x ¬ φ)
4	1, 3	bitr4i 243	1 ⊢ (∃xφ ↔ φ)

Syntax hints:  ¬ wn 3   ↔ 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

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

This theorem is referenced by: (None)