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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 34939, bj-2uplth 34948, bj-2uplex 34949, and the properties of the projections (see df-bj-pr1 34928 and df-bj-pr2 34942). (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 34924 | . 2 class ⦅𝐴⦆ |
3 | c0 4237 | . . . 4 class ∅ | |
4 | 3 | csn 4541 | . . 3 class {∅} |
5 | 1 | bj-ctag 34901 | . . 3 class tag 𝐴 |
6 | 4, 5 | cxp 5549 | . 2 class ({∅} × tag 𝐴) |
7 | 2, 6 | wceq 1543 | 1 wff ⦅𝐴⦆ = ({∅} × tag 𝐴) |
Colors of variables: wff setvar class |
This definition is referenced by: bj-1upleq 34926 bj-pr11val 34932 bj-1uplex 34935 bj-1upln0 34936 bj-pr22val 34946 bj-2upln1upl 34951 |
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