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 4695 | . 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴} | |
2 | dfsn2 4578 | . 2 ⊢ {𝐴} = {𝐴, 𝐴} | |
3 | 1, 2 | eqtr4i 2767 | 1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 {csn 4565 {cpr 4567 {ctp 4569 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 846 df-tru 1542 df-ex 1780 df-sb 2066 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3439 df-un 3897 df-pr 4568 df-tp 4570 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |