Theorem 19.9tOLD 1857

Description: Obsolete proof of 19.9t 1779 as of 30-Dec-2017. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.)(New usage is discouraged.)

Assertion

Ref	Expression
19.9tOLD	|- ( F/xph -> (E.xph <-> ph))

Proof of Theorem 19.9tOLD

Step	Hyp	Ref	Expression
1		df-ex 1542	. . 3 |- (E.xph <-> -. A.x -. ph)
2		id 19	. . . . . 6 |- ( F/xph -> F/xph)
3	2	nfnd 1791	. . . . 5 |- ( F/xph -> F/x -. ph)
4	3	nfrd 1763	. . . 4 |- ( F/xph -> (-. ph -> A.x -. ph))
5	4	con1d 116	. . 3 |- ( F/xph -> (-. A.x -. ph -> ph))
6	1, 5	syl5bi 208	. 2 |- ( F/xph -> (E.xph -> ph))
7		19.8a 1756	. 2 |- (ph -> E.xph)
8	6, 7	impbid1 194	1 |- ( F/xph -> (E.xph <-> ph))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176  A.wal 1540  E.wex 1541   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)