Description: When R is a relation, the sethood assumptions on brcnv can be omitted. (Contributed by Mario Carneiro, 28-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | relbrcnv.1 | ⊢ Rel 𝑅 | |
Assertion | relbrcnv | ⊢ ( 𝐴 ◡ 𝑅 𝐵 ↔ 𝐵 𝑅 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relbrcnv.1 | ⊢ Rel 𝑅 | |
2 | relbrcnvg | ⊢ ( Rel 𝑅 → ( 𝐴 ◡ 𝑅 𝐵 ↔ 𝐵 𝑅 𝐴 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐴 ◡ 𝑅 𝐵 ↔ 𝐵 𝑅 𝐴 ) |