Theorem exbidh 1593

Description: Formula-building rule for existential quantifier (deduction form). (Contributed by NM, 5-Aug-1993.)

Hypotheses

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

Assertion

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

Proof of Theorem exbidh

Step	Hyp	Ref	Expression
1		exbidh.1	. . 3 |- ( ph -> A. x ph )
2		exbidh.2	. . 3 |- ( ph -> ( ps <-> ch ) )
3	1, 2	alrimih 1445	. 2 |- ( ph -> A. x ( ps <-> ch ) )
4		exbi 1583	. 2 |- ( A. x ( ps <-> ch ) -> ( E. x ps <-> E. x ch ) )
5	3, 4	syl 14	1 |- ( ph -> ( E. x ps <-> E. x ch ) )

Syntax hints:   -> wi 4   <-> wb 104   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-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exbid  1595  drex2  1710  drex1  1770  exbidv  1797  mobidh  2031