Theorem 19.9OLD 2205

Description: Obsolete proof of 19.9 2072 as of 6-Oct-2021. (Contributed by FL, 24-Mar-2007.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) Revised to shorten other proofs. (Revised by Wolf Lammen, 14-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.9OLD.1	|- F/ x ph

Assertion

Ref	Expression
19.9OLD	|- ( E. x ph <-> ph )

Proof of Theorem 19.9OLD

Step	Hyp	Ref	Expression
1		19.9OLD.1	. 2 |- F/ x ph
2		19.9tOLD 2204	. 2 |- ( F/ x ph -> ( E. x ph <-> ph ) )
3	1, 2	ax-mp 5	1 |- ( E. x ph <-> ph )

Syntax hints:   <-> wb 196   E.wex 1704   F/wnfOLD 1709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nfOLD 1721

This theorem is referenced by:  19.9hOLD  2206  exlimdOLD  2223