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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 3435 | . . 3 ⊢ 𝑥 ∈ V | |
2 | 1 | eltp 4527 | . 2 ⊢ (𝑥 ∈ {𝐴, 𝐵, 𝐶} ↔ (𝑥 = 𝐴 ∨ 𝑥 = 𝐵 ∨ 𝑥 = 𝐶)) |
3 | 2 | abbi2i 2920 | 1 ⊢ {𝐴, 𝐵, 𝐶} = {𝑥 ∣ (𝑥 = 𝐴 ∨ 𝑥 = 𝐵 ∨ 𝑥 = 𝐶)} |
Colors of variables: wff setvar class |
Syntax hints: ∨ w3o 1077 = wceq 1520 {cab 2773 {ctp 4470 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1775 ax-4 1789 ax-5 1886 ax-6 1945 ax-7 1990 ax-8 2081 ax-9 2089 ax-10 2110 ax-11 2124 ax-12 2139 ax-ext 2767 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-3or 1079 df-tru 1523 df-ex 1760 df-nf 1764 df-sb 2041 df-clab 2774 df-cleq 2786 df-clel 2861 df-nfc 2933 df-v 3434 df-un 3859 df-sn 4467 df-pr 4469 df-tp 4471 |
This theorem is referenced by: tprot 4586 en3lplem2 8911 tpid3gVD 40667 en3lplem2VD 40669 |
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