Definition df-bj-1upl 37833

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 37847, bj-2uplth 37856, bj-2uplex 37857, and the properties of the projections (see df-bj-pr1 37836 and df-bj-pr2 37850). (Contributed by BJ, 6-Apr-2019.) (New usage is discouraged.)

Assertion

Ref	Expression
df-bj-1upl	⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴)

Detailed syntax breakdown of Definition df-bj-1upl

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2	1	bj-c1upl 37832	. 2 class ⦅𝐴⦆
3		c0 4278	. . . 4 class ∅
4	3	csn 4583	. . 3 class {∅}
5	1	bj-ctag 37809	. . 3 class tag 𝐴
6	4, 5	cxp 5645	. 2 class ({∅} × tag 𝐴)
7	2, 6	wceq 1570	1 wff ⦅𝐴⦆ = ({∅} × tag 𝐴)

This definition is used by:  bj-1upleq  37834  bj-pr11val  37840  bj-1uplex  37843  bj-1upln0  37844  bj-pr22val  37854  bj-2upln1upl  37859