Theorem 19.21vOLDOLD 1789

Description: Obsolete proof of 19.21v 1788 as of 12-Jul-2020. (Contributed by NM, 21-Jun-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 2-Jan-2020.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
19.21vOLDOLD	|- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.21vOLDOLD

Step	Hyp	Ref	Expression
1		ax-5 1760	. . 3 |- ( ph -> A. x ph )
2		alim 1685	. . 3 |- ( A. x ( ph -> ps ) -> ( A. x ph -> A. x ps ) )
3	1, 2	syl5 33	. 2 |- ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) )
4		ax5e 1762	. . . 4 |- ( E. x ph -> ph )
5	4	imim1i 60	. . 3 |- ( ( ph -> A. x ps ) -> ( E. x ph -> A. x ps ) )
6		19.38 1714	. . 3 |- ( ( E. x ph -> A. x ps ) -> A. x ( ph -> ps ) )
7	5, 6	syl 17	. 2 |- ( ( ph -> A. x ps ) -> A. x ( ph -> ps ) )
8	3, 7	impbii 191	1 |- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 188   A.wal 1444   E.wex 1665

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760

This theorem depends on definitions:  df-bi 189  df-ex 1666

This theorem is referenced by: (None)