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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 4683 | . 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴} | |
2 | dfsn2 4570 | . 2 ⊢ {𝐴} = {𝐴, 𝐴} | |
3 | 1, 2 | eqtr4i 2844 | 1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 {csn 4557 {cpr 4559 {ctp 4561 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-v 3494 df-un 3938 df-pr 4560 df-tp 4562 |
This theorem is referenced by: (None) |
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