![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > tpidm12 | GIF version |
Description: Unordered triple {𝐴, 𝐴, 𝐵} is just an overlong way to write {𝐴, 𝐵}. (Contributed by David A. Wheeler, 10-May-2015.) |
Ref | Expression |
---|---|
tpidm12 | ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 3621 | . . 3 ⊢ {𝐴} = {𝐴, 𝐴} | |
2 | 1 | uneq1i 3300 | . 2 ⊢ ({𝐴} ∪ {𝐵}) = ({𝐴, 𝐴} ∪ {𝐵}) |
3 | df-pr 3614 | . 2 ⊢ {𝐴, 𝐵} = ({𝐴} ∪ {𝐵}) | |
4 | df-tp 3615 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = ({𝐴, 𝐴} ∪ {𝐵}) | |
5 | 2, 3, 4 | 3eqtr4ri 2221 | 1 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵} |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 ∪ cun 3142 {csn 3607 {cpr 3608 {ctp 3609 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-pr 3614 df-tp 3615 |
This theorem is referenced by: tpidm13 3707 tpidm23 3708 tpidm 3709 |
Copyright terms: Public domain | W3C validator |