Description: The rationals form a division ring. (Contributed by Mario Carneiro, 8-Sep-2014)
Ref | Expression | ||
---|---|---|---|
Hypothesis | qrng.q | ⊢ 𝑄 = ( ℂfld ↾s ℚ ) | |
Assertion | qdrng | ⊢ 𝑄 ∈ DivRing |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qrng.q | ⊢ 𝑄 = ( ℂfld ↾s ℚ ) | |
2 | qsubdrg | ⊢ ( ℚ ∈ ( SubRing ‘ ℂfld ) ∧ ( ℂfld ↾s ℚ ) ∈ DivRing ) | |
3 | 2 | simpri | ⊢ ( ℂfld ↾s ℚ ) ∈ DivRing |
4 | 1 3 | eqeltri | ⊢ 𝑄 ∈ DivRing |