Theorem 3exbidv

Description: Formula-building rule for three existential quantifiers (deduction form). (Contributed by NM, 1-May-1995)

	Ref	Expression
Hypothesis	3exbidv.1	|- ( ph -> ( ps <-> ch ) )
Assertion	3exbidv	|- ( ph -> ( E. x E. y E. z ps <-> E. x E. y E. z ch ) )

Proof

Step	Hyp	Ref	Expression
1		3exbidv.1	|- ( ph -> ( ps <-> ch ) )
2	1	exbidv	|- ( ph -> ( E. z ps <-> E. z ch ) )
3	2	2exbidv	|- ( ph -> ( E. x E. y E. z ps <-> E. x E. y E. z ch ) )