|   | Mathbox for BJ | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-1upl | Structured version Visualization version GIF version | ||
| Description: Definition of the Morse monuple (1-tuple). This is not useful per se, but is used as a step towards the definition of couples (2-tuples, or ordered pairs). The reason for "tagging" the set is so that an m-tuple and an n-tuple be equal only when m = n. Note that with this definition, the 0-tuple is the empty set. New usage is discouraged because the precise definition is generally unimportant compared to the characteristic properties bj-2upleq 37014, bj-2uplth 37023, bj-2uplex 37024, and the properties of the projections (see df-bj-pr1 37003 and df-bj-pr2 37017). (Contributed by BJ, 6-Apr-2019.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| df-bj-1upl | ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | cA | . . 3 class 𝐴 | |
| 2 | 1 | bj-c1upl 36999 | . 2 class ⦅𝐴⦆ | 
| 3 | c0 4332 | . . . 4 class ∅ | |
| 4 | 3 | csn 4625 | . . 3 class {∅} | 
| 5 | 1 | bj-ctag 36976 | . . 3 class tag 𝐴 | 
| 6 | 4, 5 | cxp 5682 | . 2 class ({∅} × tag 𝐴) | 
| 7 | 2, 6 | wceq 1539 | 1 wff ⦅𝐴⦆ = ({∅} × tag 𝐴) | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: bj-1upleq 37001 bj-pr11val 37007 bj-1uplex 37010 bj-1upln0 37011 bj-pr22val 37021 bj-2upln1upl 37026 | 
| Copyright terms: Public domain | W3C validator |