Theorem 19.23h 1993

Description: Theorem 19.23 of [Margaris] p. 90. See 19.23 1992. (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 1673	. 2 |- F/ x ps
3	2	19.23 1992	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 188   A.wal 1441   E.wex 1662

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667

This theorem is referenced by:  equsalhw  2027