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| Mirrors > Home > MPE Home > Th. List > opelxpi | Structured version Visualization version GIF version | ||
| Description: Ordered pair membership in a Cartesian product (implication). (Contributed by NM, 28-May-1995.) |
| Ref | Expression |
|---|---|
| opelxpi | ⊢ ((𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐷) → 〈𝐴, 𝐵〉 ∈ (𝐶 × 𝐷)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | opelxp 5721 | . 2 ⊢ (〈𝐴, 𝐵〉 ∈ (𝐶 × 𝐷) ↔ (𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐷)) | |
| 2 | 1 | biimpri 228 | 1 ⊢ ((𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐷) → 〈𝐴, 𝐵〉 ∈ (𝐶 × 𝐷)) |
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