![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 4754 | . 2 ⊢ {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴} | |
2 | tpidm12 4760 | . 2 ⊢ {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴} | |
3 | prcom 4737 | . 2 ⊢ {𝐵, 𝐴} = {𝐴, 𝐵} | |
4 | 1, 2, 3 | 3eqtri 2767 | 1 ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 {cpr 4633 {ctp 4635 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3or 1087 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-un 3968 df-sn 4632 df-pr 4634 df-tp 4636 |
This theorem is referenced by: tppreq3 4764 fntpb 7229 hashtpg 14521 hash3tpde 14529 |
Copyright terms: Public domain | W3C validator |