Theorem 19.23h 2014

Description: Theorem 19.23 of [Margaris] p. 90. See 19.23 2013. (Contributed by NM, 24-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)

Hypothesis

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

Assertion

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

Proof of Theorem 19.23h

Step	Hyp	Ref	Expression
1		19.23h.1	. . 3 |- ( ps -> A. x ps )
2	1	nfi 1682	. 2 |- F/ x ps
3	2	19.23 2013	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 189   A.wal 1450   E.wex 1671

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950

This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676

This theorem is referenced by:  equsalhw  2047