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| Mirrors > Home > MPE Home > Th. List > elssuni | Structured version Visualization version GIF version | ||
| Description: An element of a class is a subclass of its union. Theorem 8.6 of [Quine] p. 54. Also the basis for Proposition 7.20 of [TakeutiZaring] p. 40. (Contributed by NM, 6-Jun-1994.) |
| Ref | Expression |
|---|---|
| elssuni | ⊢ (𝐴 ∈ 𝐵 → 𝐴 ⊆ ∪ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssid 4006 | . 2 ⊢ 𝐴 ⊆ 𝐴 | |
| 2 | ssuni 4932 | . 2 ⊢ ((𝐴 ⊆ 𝐴 ∧ 𝐴 ∈ 𝐵) → 𝐴 ⊆ ∪ 𝐵) | |
| 3 | 1, 2 | mpan 690 | 1 ⊢ (𝐴 ∈ 𝐵 → 𝐴 ⊆ ∪ 𝐵) |
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