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Mirrors > Home > MPE Home > Th. List > tpcomb | Structured version Visualization version GIF version |
Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.) |
Ref | Expression |
---|---|
tpcomb | ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tpcoma 4285 | . 2 ⊢ {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴} | |
2 | tprot 4284 | . 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴} | |
3 | tprot 4284 | . 2 ⊢ {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴} | |
4 | 1, 2, 3 | 3eqtr4i 2654 | 1 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 {ctp 4181 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-sn 4178 df-pr 4180 df-tp 4182 |
This theorem is referenced by: f13dfv 6530 frgr3v 27139 signswch 30638 signstfvcl 30650 dvh4dimN 36736 |
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