Metamath Proof Explorer


Theorem zlmmulrOLD

Description: Obsolete version of zlmbas as of 3-Nov-2024. Ring operation of a ZZ -module (if present). (Contributed by Mario Carneiro, 2-Oct-2015) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Hypotheses zlmbas.w W=ℤModG
zlmmulr.2 ·˙=G
Assertion zlmmulrOLD ·˙=W

Proof

Step Hyp Ref Expression
1 zlmbas.w W=ℤModG
2 zlmmulr.2 ·˙=G
3 df-mulr 𝑟=Slot3
4 3nn 3
5 3lt5 3<5
6 1 3 4 5 zlmlemOLD G=W
7 2 6 eqtri ·˙=W