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| Mirrors > Home > MPE Home > Th. List > opex | Structured version Visualization version GIF version | ||
| Description: An ordered pair of classes is a set. Exercise 7 of [TakeutiZaring] p. 16. (Contributed by NM, 18-Aug-1993.) (Revised by Mario Carneiro, 26-Apr-2015.) |
| Ref | Expression |
|---|---|
| opex | ⊢ 〈𝐴, 𝐵〉 ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dfopif 4870 | . 2 ⊢ 〈𝐴, 𝐵〉 = if((𝐴 ∈ V ∧ 𝐵 ∈ V), {{𝐴}, {𝐴, 𝐵}}, ∅) | |
| 2 | prex 5437 | . . 3 ⊢ {{𝐴}, {𝐴, 𝐵}} ∈ V | |
| 3 | 0ex 5307 | . . 3 ⊢ ∅ ∈ V | |
| 4 | 2, 3 | ifex 4576 | . 2 ⊢ if((𝐴 ∈ V ∧ 𝐵 ∈ V), {{𝐴}, {𝐴, 𝐵}}, ∅) ∈ V |
| 5 | 1, 4 | eqeltri 2837 | 1 ⊢ 〈𝐴, 𝐵〉 ∈ V |
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