New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > dfsn2 | GIF version |
Description: Alternate definition of singleton. Definition 5.1 of [TakeutiZaring] p. 15. (Contributed by NM, 24-Apr-1994.) |
Ref | Expression |
---|---|
dfsn2 | ⊢ {A} = {A, A} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 3742 | . 2 ⊢ {A, A} = ({A} ∪ {A}) | |
2 | unidm 3407 | . 2 ⊢ ({A} ∪ {A}) = {A} | |
3 | 1, 2 | eqtr2i 2374 | 1 ⊢ {A} = {A, A} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ∪ cun 3207 {csn 3737 {cpr 3738 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-pr 3742 |
This theorem is referenced by: nfsn 3784 tpidm12 3821 tpidm 3824 unisn 3907 intsng 3961 |
Copyright terms: Public domain | W3C validator |