Theorem exlimdOLD 2223

Description: Obsolete proof of exlimd 2087 as of 6-Oct-2021. (Contributed by NM, 23-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 12-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
exlimdOLD.1	|- F/ x ph
exlimdOLD.2	|- F/ x ch
exlimdOLD.3	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
exlimdOLD	|- ( ph -> ( E. x ps -> ch ) )

Proof of Theorem exlimdOLD

Step	Hyp	Ref	Expression
1		exlimdOLD.1	. . 3 |- F/ x ph
2		exlimdOLD.3	. . 3 |- ( ph -> ( ps -> ch ) )
3	1, 2	eximdOLD 2197	. 2 |- ( ph -> ( E. x ps -> E. x ch ) )
4		exlimdOLD.2	. . 3 |- F/ x ch
5	4	19.9OLD 2205	. 2 |- ( E. x ch <-> ch )
6	3, 5	syl6ib 241	1 |- ( ph -> ( E. x ps -> ch ) )

Syntax hints:   -> wi 4   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:  exlimdhOLD  2224