Description: Membership in a domain. Theorem 4 of Suppes p. 59. (Contributed by NM, 2-Apr-2004)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eldm.1 | ⊢ 𝐴 ∈ V | |
Assertion | eldm | ⊢ ( 𝐴 ∈ dom 𝐵 ↔ ∃ 𝑦 𝐴 𝐵 𝑦 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldm.1 | ⊢ 𝐴 ∈ V | |
2 | eldmg | ⊢ ( 𝐴 ∈ V → ( 𝐴 ∈ dom 𝐵 ↔ ∃ 𝑦 𝐴 𝐵 𝑦 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐴 ∈ dom 𝐵 ↔ ∃ 𝑦 𝐴 𝐵 𝑦 ) |