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Metamath Proof Explorer
Description: The set of complex numbers is the base set of the complex left module of
complex numbers. (Contributed by AV, 21-Sep-2021)
|
|
Ref |
Expression |
|
Hypothesis |
cnrlmod.c |
⊢ 𝐶 = ( ringLMod ‘ ℂfld ) |
|
Assertion |
cnrbas |
⊢ ( Base ‘ 𝐶 ) = ℂ |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
cnrlmod.c |
⊢ 𝐶 = ( ringLMod ‘ ℂfld ) |
| 2 |
|
rlmbas |
⊢ ( Base ‘ ℂfld ) = ( Base ‘ ( ringLMod ‘ ℂfld ) ) |
| 3 |
|
cnfldbas |
⊢ ℂ = ( Base ‘ ℂfld ) |
| 4 |
1
|
fveq2i |
⊢ ( Base ‘ 𝐶 ) = ( Base ‘ ( ringLMod ‘ ℂfld ) ) |
| 5 |
2 3 4
|
3eqtr4ri |
⊢ ( Base ‘ 𝐶 ) = ℂ |