Theorem exlimihOLD 2222

Description: Obsolete proof of exlimih 2148 as of 6-Oct-2021. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
exlimihOLD.1	|- ( ps -> A. x ps )
exlimihOLD.2	|- ( ph -> ps )

Assertion

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

Proof of Theorem exlimihOLD

Step	Hyp	Ref	Expression
1		exlimihOLD.1	. . 3 |- ( ps -> A. x ps )
2	1	nfiOLD 1734	. 2 |- F/ x ps
3		exlimihOLD.2	. 2 |- ( ph -> ps )
4	2, 3	exlimiOLD 2221	1 |- ( E. x ph -> ps )

Syntax hints:   -> wi 4   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)