Theorem 19.23ht 1511

Description: Closed form of Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 7-Nov-2005.) (Revised by Mario Carneiro, 1-Feb-2015.)

Assertion

Ref	Expression
19.23ht	|- ( A. x ( ps -> A. x ps ) -> ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) )

Proof of Theorem 19.23ht

Step	Hyp	Ref	Expression
1		ax-ie2 1508	1 |- ( A. x ( ps -> A. x ps ) -> ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1362   E.wex 1506

This theorem was proved from axioms:  ax-ie2 1508

This theorem is referenced by:  19.23h  1512  exlimd2  1609  19.9ht  1655