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| Mirrors > Home > MPE Home > Th. List > dftp2 | Structured version Visualization version GIF version | ||
| Description: Alternate definition of unordered triple of classes. Special case of Definition 5.3 of [TakeutiZaring] p. 16. (Contributed by NM, 8-Apr-1994.) |
| Ref | Expression |
|---|---|
| dftp2 | ⊢ {𝐴, 𝐵, 𝐶} = {𝑥 ∣ (𝑥 = 𝐴 ∨ 𝑥 = 𝐵 ∨ 𝑥 = 𝐶)} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | vex 3484 | . . 3 ⊢ 𝑥 ∈ V | |
| 2 | 1 | eltp 4689 | . 2 ⊢ (𝑥 ∈ {𝐴, 𝐵, 𝐶} ↔ (𝑥 = 𝐴 ∨ 𝑥 = 𝐵 ∨ 𝑥 = 𝐶)) |
| 3 | 2 | eqabi 2877 | 1 ⊢ {𝐴, 𝐵, 𝐶} = {𝑥 ∣ (𝑥 = 𝐴 ∨ 𝑥 = 𝐵 ∨ 𝑥 = 𝐶)} |
| Colors of variables: wff setvar class |
| Syntax hints: ∨ w3o 1086 = wceq 1540 {cab 2714 {ctp 4630 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3or 1088 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-un 3956 df-sn 4627 df-pr 4629 df-tp 4631 |
| This theorem is referenced by: tprot 4749 en3lplem2 9653 rabsstp 32521 abtp 43423 tpid3gVD 44862 en3lplem2VD 44864 |
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