Theorem iscnrm3lem6

Description: Lemma for iscnrm3lem7 . (Contributed by Zhi Wang, 5-Sep-2024)

	Ref	Expression
Hypothesis	iscnrm3lem6.1	|- ( ( ph /\ ( x e. V /\ y e. W ) /\ ps ) -> ch )
Assertion	iscnrm3lem6	|- ( ph -> ( E. x e. V E. y e. W ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		iscnrm3lem6.1	|- ( ( ph /\ ( x e. V /\ y e. W ) /\ ps ) -> ch )
2	1	3exp	|- ( ph -> ( ( x e. V /\ y e. W ) -> ( ps -> ch ) ) )
3	2	rexlimdvv	|- ( ph -> ( E. x e. V E. y e. W ps -> ch ) )