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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 3477 | . . 3 ⊢ 𝑥 ∈ V | |
2 | 1 | eltp 4692 | . 2 ⊢ (𝑥 ∈ {𝐴, 𝐵, 𝐶} ↔ (𝑥 = 𝐴 ∨ 𝑥 = 𝐵 ∨ 𝑥 = 𝐶)) |
3 | 2 | eqabi 2868 | 1 ⊢ {𝐴, 𝐵, 𝐶} = {𝑥 ∣ (𝑥 = 𝐴 ∨ 𝑥 = 𝐵 ∨ 𝑥 = 𝐶)} |
Colors of variables: wff setvar class |
Syntax hints: ∨ w3o 1085 = wceq 1540 {cab 2708 {ctp 4632 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3or 1087 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3475 df-un 3953 df-sn 4629 df-pr 4631 df-tp 4633 |
This theorem is referenced by: tprot 4753 en3lplem2 9614 abtp 42623 tpid3gVD 44065 en3lplem2VD 44067 |
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