Description: A function maps its domain onto its range. (Contributed by NM, 23-Jul-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | funforn | ⊢ ( Fun 𝐴 ↔ 𝐴 : dom 𝐴 –onto→ ran 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfn | ⊢ ( Fun 𝐴 ↔ 𝐴 Fn dom 𝐴 ) | |
2 | dffn4 | ⊢ ( 𝐴 Fn dom 𝐴 ↔ 𝐴 : dom 𝐴 –onto→ ran 𝐴 ) | |
3 | 1 2 | bitri | ⊢ ( Fun 𝐴 ↔ 𝐴 : dom 𝐴 –onto→ ran 𝐴 ) |