Theorem 19.23hOLD 2220

Description: Obsolete proof of 19.23h 2122 as of 6-Oct-2021. (Contributed by NM, 24-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.23hOLD.1	|- ( ps -> A. x ps )

Assertion

Ref	Expression
19.23hOLD	|- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Proof of Theorem 19.23hOLD

Step	Hyp	Ref	Expression
1		19.23hOLD.1	. . 3 |- ( ps -> A. x ps )
2	1	nfiOLD 1734	. 2 |- F/ x ps
3	2	19.23OLD 2219	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704

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-or 385  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by: (None)