Theorem 19.8wOLD 1693

Description: Obsolete version of 19.8w 1660 as of 4-Dec-2017. (Contributed by NM, 1-Aug-2017.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
19.8wOLD.1	|- (ph -> A.xph)

Assertion

Ref	Expression
19.8wOLD	|- (ph -> E.xph)

Proof of Theorem 19.8wOLD

Step	Hyp	Ref	Expression
1		19.8wOLD.1	. . . . 5 |- (ph -> A.xph)
2		notnot 282	. . . . 5 |- (ph <-> -. -. ph)
3	2	albii 1566	. . . . 5 |- (A.xph <-> A.x -. -. ph)
4	1, 2, 3	3imtr3i 256	. . . 4 |- (-. -. ph -> A.x -. -. ph)
5	4	spnfw 1670	. . 3 |- (A.x -. ph -> -. ph)
6	5	con2i 112	. 2 |- (ph -> -. A.x -. ph)
7		df-ex 1542	. 2 |- (E.xph <-> -. A.x -. ph)
8	6, 7	sylibr 203	1 |- (ph -> E.xph)

Syntax hints:  -. wn 3   -> wi 4  A.wal 1540  E.wex 1541

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-9 1654

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by: (None)