Theorem 19.41vvv

Description: Version of 19.41 with three quantifiers and a disjoint variable condition requiring fewer axioms. (Contributed by NM, 30-Apr-1995)

	Ref	Expression
Assertion	19.41vvv	|- ( E. x E. y E. z ( ph /\ ps ) <-> ( E. x E. y E. z ph /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.41vv	|- ( E. y E. z ( ph /\ ps ) <-> ( E. y E. z ph /\ ps ) )
2	1	exbii	|- ( E. x E. y E. z ( ph /\ ps ) <-> E. x ( E. y E. z ph /\ ps ) )
3		19.41v	|- ( E. x ( E. y E. z ph /\ ps ) <-> ( E. x E. y E. z ph /\ ps ) )
4	2 3	bitri	|- ( E. x E. y E. z ( ph /\ ps ) <-> ( E. x E. y E. z ph /\ ps ) )