Theorem exbidh

Description: Formula-building rule for existential quantifier (deduction form). (Contributed by NM, 26-May-1993)

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

Proof

Step	Hyp	Ref	Expression
1		exbidh.1	|- ( ph -> A. x ph )
2		exbidh.2	|- ( ph -> ( ps <-> ch ) )
3	2	alexbii	|- ( A. x ph -> ( E. x ps <-> E. x ch ) )
4	1 3	syl	|- ( ph -> ( E. x ps <-> E. x ch ) )