Theorem 19.2OLD 1700

Description: Obsolete version of 19.2 1659 as of 4-Dec-2017. (Contributed by NM, 2-Aug-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.2OLD	|- (A.xph -> E.xph)

Proof of Theorem 19.2OLD

Step	Hyp	Ref	Expression
1		equid 1676	. . 3 |- x = x
2	1	notnoti 115	. . . 4 |- -. -. x = x
3	2	spfalw 1672	. . 3 |- (A.x -. x = x -> -. x = x)
4	1, 3	mt2 170	. 2 |- -. A.x -. x = x
5		idd 21	. . 3 |- (x = x -> (ph -> ph))
6	5	speimfw 1645	. 2 |- (-. A.x -. x = x -> (A.xph -> E.xph))
7	4, 6	ax-mp 5	1 |- (A.xph -> 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-17 1616  ax-9 1654  ax-8 1675

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

This theorem is referenced by: (None)