Theorem 19.21tOLDOLD 2074

Description: Obsolete proof of 19.21t 2073 as of 3-Nov-2021. (Contributed by NM, 27-May-1997.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 3-Jan-2018.) df-nf 1710 changed. (Revised by Wolf Lammen, 11-Sep-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.21tOLDOLD	|- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Proof of Theorem 19.21tOLDOLD

Step	Hyp	Ref	Expression
1		nf5r 2064	. . 3 |- ( F/ x ph -> ( ph -> A. x ph ) )
2		alim 1738	. . 3 |- ( A. x ( ph -> ps ) -> ( A. x ph -> A. x ps ) )
3	1, 2	syl9 77	. 2 |- ( F/ x ph -> ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) ) )
4		19.9t 2071	. . . 4 |- ( F/ x ph -> ( E. x ph <-> ph ) )
5	4	imbi1d 331	. . 3 |- ( F/ x ph -> ( ( E. x ph -> A. x ps ) <-> ( ph -> A. x ps ) ) )
6		19.38 1766	. . 3 |- ( ( E. x ph -> A. x ps ) -> A. x ( ph -> ps ) )
7	5, 6	syl6bir 244	. 2 |- ( F/ x ph -> ( ( ph -> A. x ps ) -> A. x ( ph -> ps ) ) )
8	3, 7	impbid 202	1 |- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704   F/wnf 1708

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-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)