Theorem exlimih 2148

Description: Inference associated with 19.23 2080. See exlimiv 1858 for a version with a dv condition requiring fewer axioms. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)

Hypotheses

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

Assertion

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

Proof of Theorem exlimih

Step	Hyp	Ref	Expression
1		exlimih.1	. . 3 |- ( ps -> A. x ps )
2	1	nf5i 2024	. 2 |- F/ x ps
3		exlimih.2	. 2 |- ( ph -> ps )
4	2, 3	exlimi 2086	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

This theorem is referenced by: (None)