Description: An opposite category is a category. (Contributed by Mario Carneiro, 2-Jan-2017)
Ref | Expression | ||
---|---|---|---|
Hypothesis | oppcbas.1 | ⊢ 𝑂 = ( oppCat ‘ 𝐶 ) | |
Assertion | oppccat | ⊢ ( 𝐶 ∈ Cat → 𝑂 ∈ Cat ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oppcbas.1 | ⊢ 𝑂 = ( oppCat ‘ 𝐶 ) | |
2 | 1 | oppccatid | ⊢ ( 𝐶 ∈ Cat → ( 𝑂 ∈ Cat ∧ ( Id ‘ 𝑂 ) = ( Id ‘ 𝐶 ) ) ) |
3 | 2 | simpld | ⊢ ( 𝐶 ∈ Cat → 𝑂 ∈ Cat ) |