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Mirrors > Home > MPE Home > Th. List > tpidm23 | Structured version Visualization version GIF version |
Description: Unordered triple {𝐴, 𝐵, 𝐵} is just an overlong way to write {𝐴, 𝐵}. (Contributed by David A. Wheeler, 10-May-2015.) |
Ref | Expression |
---|---|
tpidm23 | ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tprot 4645 | . 2 ⊢ {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴} | |
2 | tpidm12 4651 | . 2 ⊢ {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴} | |
3 | prcom 4628 | . 2 ⊢ {𝐵, 𝐴} = {𝐴, 𝐵} | |
4 | 1, 2, 3 | 3eqtri 2825 | 1 ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 {cpr 4527 {ctp 4529 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3or 1085 df-tru 1541 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-v 3443 df-un 3886 df-sn 4526 df-pr 4528 df-tp 4530 |
This theorem is referenced by: tppreq3 4655 fntpb 6949 hashtpg 13839 |
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