Description: Characterization of the elements of the diagonal of a Cartesian square. (Contributed by BJ, 22-Jun-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | bj-elid7 | ⊢ ( 〈 𝐵 , 𝐶 〉 ∈ ( I ↾ 𝐴 ) ↔ ( 𝐵 ∈ 𝐴 ∧ 𝐵 = 𝐶 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br | ⊢ ( 𝐵 ( I ↾ 𝐴 ) 𝐶 ↔ 〈 𝐵 , 𝐶 〉 ∈ ( I ↾ 𝐴 ) ) | |
2 | bj-idreseqb | ⊢ ( 𝐵 ( I ↾ 𝐴 ) 𝐶 ↔ ( 𝐵 ∈ 𝐴 ∧ 𝐵 = 𝐶 ) ) | |
3 | 1 2 | bitr3i | ⊢ ( 〈 𝐵 , 𝐶 〉 ∈ ( I ↾ 𝐴 ) ↔ ( 𝐵 ∈ 𝐴 ∧ 𝐵 = 𝐶 ) ) |