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Mirrors > Home > ILE Home > Th. List > tpidm | 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 3672 | . 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴} | |
2 | dfsn2 3587 | . 2 ⊢ {𝐴} = {𝐴, 𝐴} | |
3 | 1, 2 | eqtr4i 2188 | 1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴} |
Colors of variables: wff set class |
Syntax hints: = wceq 1342 {csn 3573 {cpr 3574 {ctp 3575 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2726 df-un 3118 df-pr 3580 df-tp 3581 |
This theorem is referenced by: (None) |
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