Metamath Proof Explorer


Theorem iscnrm3lem5

Description: Lemma for iscnrm3l . (Contributed by Zhi Wang, 3-Sep-2024)

Ref Expression
Hypotheses iscnrm3lem5.1 x = S y = T φ ψ
iscnrm3lem5.2 x = S y = T χ θ
iscnrm3lem5.3 τ η ζ S V T W
iscnrm3lem5.4 τ η ζ ψ θ σ
Assertion iscnrm3lem5 τ x V y W φ χ η ζ σ

Proof

Step Hyp Ref Expression
1 iscnrm3lem5.1 x = S y = T φ ψ
2 iscnrm3lem5.2 x = S y = T χ θ
3 iscnrm3lem5.3 τ η ζ S V T W
4 iscnrm3lem5.4 τ η ζ ψ θ σ
5 1 2 imbi12d x = S y = T φ χ ψ θ
6 5 rspc2gv S V T W x V y W φ χ ψ θ
7 6 3 4 iscnrm3lem4 τ x V y W φ χ η ζ σ