Theorem eximdh 1791

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 20-May-1996.)

Hypotheses

Ref	Expression
eximdh.1	|- ( ph -> A. x ph )
eximdh.2	|- ( ph -> ( ps -> ch ) )

Assertion

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

Proof of Theorem eximdh

Step	Hyp	Ref	Expression
1		eximdh.1	. 2 |- ( ph -> A. x ph )
2		eximdh.2	. . 3 |- ( ph -> ( ps -> ch ) )
3	2	aleximi 1759	. 2 |- ( A. x ph -> ( E. x ps -> E. x ch ) )
4	1, 3	syl 17	1 |- ( ph -> ( E. x ps -> E. x ch ) )

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

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

This theorem is referenced by:  eximdv  1846  eximd  2085  eximdOLD  2197  ax6e2eq  38773