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| 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 37013, bj-2uplth 37022, bj-2uplex 37023, and the properties of the projections (see df-bj-pr1 37002 and df-bj-pr2 37016). (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 36998 | . 2 class ⦅𝐴⦆ | 
| 3 | c0 4333 | . . . 4 class ∅ | |
| 4 | 3 | csn 4626 | . . 3 class {∅} | 
| 5 | 1 | bj-ctag 36975 | . . 3 class tag 𝐴 | 
| 6 | 4, 5 | cxp 5683 | . 2 class ({∅} × tag 𝐴) | 
| 7 | 2, 6 | wceq 1540 | 1 wff ⦅𝐴⦆ = ({∅} × tag 𝐴) | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: bj-1upleq 37000 bj-pr11val 37006 bj-1uplex 37009 bj-1upln0 37010 bj-pr22val 37020 bj-2upln1upl 37025 | 
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