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BASIC ALGEBRAIC STRUCTURES
Ideals
The subring algebra; ideals
rspval
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rlmval2
Metamath Proof Explorer
Ascii
Unicode
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