Theorem 19.9hd 1640

Description: A deduction version of one direction of 19.9 1623. This is an older variation of this theorem; new proofs should use 19.9d 1639. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Hypotheses

Ref	Expression
19.9hd.1	|- ( ps -> A. x ps )
19.9hd.2	|- ( ps -> ( ph -> A. x ph ) )

Assertion

Ref	Expression
19.9hd	|- ( ps -> ( E. x ph -> ph ) )

Proof of Theorem 19.9hd

Step	Hyp	Ref	Expression
1		19.9hd.1	. 2 |- ( ps -> A. x ps )
2		19.9hd.2	. . 3 |- ( ps -> ( ph -> A. x ph ) )
3	2	alimi 1431	. 2 |- ( A. x ps -> A. x ( ph -> A. x ph ) )
4		19.9ht 1620	. 2 |- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> ph ) )
5	1, 3, 4	3syl 17	1 |- ( ps -> ( E. x ph -> ph ) )

Syntax hints:   -> wi 4   A.wal 1329   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1423  ax-gen 1425  ax-ie2 1470

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  sbiedh  1760  bj-sbimedh  12978