![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > tpidm | Structured version Visualization version GIF version |
Description: Unordered triple {𝐴, 𝐴, 𝐴} is just an overlong way to write {𝐴}. (Contributed by David A. Wheeler, 10-May-2015.) |
Ref | Expression |
---|---|
tpidm | ⊢ {𝐴, 𝐴, 𝐴} = {𝐴} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tpidm12 4753 | . 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴} | |
2 | dfsn2 4636 | . 2 ⊢ {𝐴} = {𝐴, 𝐴} | |
3 | 1, 2 | eqtr4i 2763 | 1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 {csn 4623 {cpr 4625 {ctp 4627 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-v 3476 df-un 3950 df-pr 4626 df-tp 4628 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |