Theorem 19.9dOLD 2203

Description: Obsolete proof of 19.9d 2070 as of 6-Oct-2021. (Contributed by NM, 14-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) Revised to shorten other proofs. (Revised by Wolf Lammen, 14-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.9dOLD.1	|- ( ps -> F/ x ph )

Assertion

Ref	Expression
19.9dOLD	|- ( ps -> ( E. x ph -> ph ) )

Proof of Theorem 19.9dOLD

Step	Hyp	Ref	Expression
1		19.9dOLD.1	. . 3 |- ( ps -> F/ x ph )
2		df-nfOLD 1721	. . 3 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
3	1, 2	sylib 208	. 2 |- ( ps -> A. x ( ph -> A. x ph ) )
4		19.9ht 2143	. 2 |- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> ph ) )
5	3, 4	syl 17	1 |- ( ps -> ( E. x ph -> ph ) )

Syntax hints:   -> wi 4   A.wal 1481   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:  19.9tOLD  2204