Theorem 2exbidv

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

	Ref	Expression
Hypothesis	2albidv.1	|- ( ph -> ( ps <-> ch ) )
Assertion	2exbidv	|- ( ph -> ( E. x E. y ps <-> E. x E. y ch ) )

Proof

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