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| Mirrors > Home > MPE Home > Th. List > prssi | Structured version Visualization version GIF version | ||
| Description: A pair of elements of a class is a subset of the class. (Contributed by NM, 16-Jan-2015.) |
| Ref | Expression |
|---|---|
| prssi | ⊢ ((𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶) → {𝐴, 𝐵} ⊆ 𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | prssg 4819 | . 2 ⊢ ((𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶) → ((𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶) ↔ {𝐴, 𝐵} ⊆ 𝐶)) | |
| 2 | 1 | ibi 267 | 1 ⊢ ((𝐴 ∈ 𝐶 ∧ 𝐵 ∈ 𝐶) → {𝐴, 𝐵} ⊆ 𝐶) |
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