Theorem exbidh 1505

Description: Formula-building rule for existential quantifier (deduction rule). (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 1358	. 2 |- ( ph -> A. x ( ps <-> ch ) )
4		exbi 1495	. 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 98   A.wal 1241   E.wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  exbid  1507  drex2  1620  drex1  1679  exbidv  1706  mobidh  1934