Metamath Proof Explorer


Definition df-bj-1upl

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

Ref Expression
Assertion df-bj-1upl
|- (| A |) = ( { (/) } X. tag A )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA
 |-  A
1 0 bj-c1upl
 |-  (| A |)
2 c0
 |-  (/)
3 2 csn
 |-  { (/) }
4 0 bj-ctag
 |-  tag A
5 3 4 cxp
 |-  ( { (/) } X. tag A )
6 1 5 wceq
 |-  (| A |) = ( { (/) } X. tag A )