Theorem 19.9v 1664

Description: Special case of Theorem 19.9 of [Margaris] p. 89. (Contributed by NM, 28-May-1995.) (Revised by NM, 1-Aug-2017.) (Revised by Wolf Lammen to remove dependency on ax-8, 4-Dec-2017.)

Assertion

Ref	Expression
19.9v	|- (E.xph <-> ph)

Distinct variable group:   ph,x

Proof of Theorem 19.9v

Step	Hyp	Ref	Expression
1		ax17e 1618	. 2 |- (E.xph -> ph)
2		ax-17 1616	. . 3 |- (ph -> A.xph)
3	2	19.8w 1660	. 2 |- (ph -> E.xph)
4	1, 3	impbii 180	1 |- (E.xph <-> ph)

Syntax hints:   <-> wb 176  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

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

This theorem is referenced by:  19.3v  1665  exlimivOLD  1698