Metamath Proof Explorer


Theorem iscnrm3lem7

Description: Lemma for iscnrm3rlem8 and iscnrm3llem2 involving restricted existential quantifications. (Contributed by Zhi Wang, 5-Sep-2024)

Ref Expression
Hypotheses iscnrm3lem7.1 z = Z χ θ
iscnrm3lem7.2 w = W θ τ
iscnrm3lem7.3 φ x A y B ψ Z C W D τ
Assertion iscnrm3lem7 φ x A y B ψ z C w D χ

Proof

Step Hyp Ref Expression
1 iscnrm3lem7.1 z = Z χ θ
2 iscnrm3lem7.2 w = W θ τ
3 iscnrm3lem7.3 φ x A y B ψ Z C W D τ
4 1 2 rspc2ev Z C W D τ z C w D χ
5 3 4 syl φ x A y B ψ z C w D χ
6 5 iscnrm3lem6 φ x A y B ψ z C w D χ