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Mirrors > Home > NFE Home > Th. List > tprot | GIF version |
Description: Rotation of the elements of an unordered triple. (Contributed by Alan Sare, 24-Oct-2011.) |
Ref | Expression |
---|---|
tprot | ⊢ {A, B, C} = {B, C, A} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3orrot 940 | . . 3 ⊢ ((x = A ∨ x = B ∨ x = C) ↔ (x = B ∨ x = C ∨ x = A)) | |
2 | 1 | abbii 2465 | . 2 ⊢ {x ∣ (x = A ∨ x = B ∨ x = C)} = {x ∣ (x = B ∨ x = C ∨ x = A)} |
3 | dftp2 3772 | . 2 ⊢ {A, B, C} = {x ∣ (x = A ∨ x = B ∨ x = C)} | |
4 | dftp2 3772 | . 2 ⊢ {B, C, A} = {x ∣ (x = B ∨ x = C ∨ x = A)} | |
5 | 2, 3, 4 | 3eqtr4i 2383 | 1 ⊢ {A, B, C} = {B, C, A} |
Colors of variables: wff setvar class |
Syntax hints: ∨ w3o 933 = wceq 1642 {cab 2339 {ctp 3739 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3or 935 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-tp 3743 |
This theorem is referenced by: tpcomb 3817 tpass 3818 tpidm13 3822 tpidm23 3823 |
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