Theorem exbidh 1614

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 1469	. 2 |- ( ph -> A. x ( ps <-> ch ) )
4		exbi 1604	. 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 105   A.wal 1351   E.wex 1492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exbid  1616  drex2  1732  drex1  1798  exbidv  1825  mobidh  2060