Description: An onto function implies dominance of domain over range. (Contributed by NM, 23-Jul-2004)
Ref | Expression | ||
---|---|---|---|
Hypothesis | fodom.1 | ⊢ 𝐴 ∈ V | |
Assertion | fodom | ⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 → 𝐵 ≼ 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fodom.1 | ⊢ 𝐴 ∈ V | |
2 | fodomg | ⊢ ( 𝐴 ∈ V → ( 𝐹 : 𝐴 –onto→ 𝐵 → 𝐵 ≼ 𝐴 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 → 𝐵 ≼ 𝐴 ) |