Theorem 19.39 1899

Description: Theorem 19.39 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Assertion

Ref	Expression
19.39	|- ( ( E. x ph -> E. x ps ) -> E. x ( ph -> ps ) )

Proof of Theorem 19.39

Step	Hyp	Ref	Expression
1		19.2 1892	. . 3 |- ( A. x ph -> E. x ph )
2	1	imim1i 63	. 2 |- ( ( E. x ph -> E. x ps ) -> ( A. x ph -> E. x ps ) )
3		19.35 1805	. 2 |- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
4	2, 3	sylibr 224	1 |- ( ( E. x ph -> E. x ps ) -> E. x ( ph -> ps ) )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)