Metamath Proof Explorer


Theorem rspval

Description: Value of the ring span function. (Contributed by Stefan O'Rear, 4-Apr-2015)

Ref Expression
Assertion rspval RSpan W = LSpan ringLMod W

Proof

Step Hyp Ref Expression
1 df-rsp RSpan = LSpan ringLMod
2 1 fveq1i RSpan W = LSpan ringLMod W
3 00lsp = LSpan
4 rlmfn ringLMod Fn V
5 fnfun ringLMod Fn V Fun ringLMod
6 4 5 ax-mp Fun ringLMod
7 3 6 fvco4i LSpan ringLMod W = LSpan ringLMod W
8 2 7 eqtri RSpan W = LSpan ringLMod W