Theorem exbidh 1794

Description: Formula-building rule for existential quantifier (deduction rule). (Contributed by NM, 26-May-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	. 2 |- ( ph -> A. x ph )
2		exbidh.2	. . 3 |- ( ph -> ( ps <-> ch ) )
3	2	alexbii 1760	. 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   <-> wb 196   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:  exbidv  1850  exbid  2091  exbidOLD  2200  drex2  2328  ac6s6  33980