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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-2upl | Structured version Visualization version GIF version |
Description: Definition of the Morse couple. See df-bj-1upl 34925. 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-Oct-2018.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-bj-2upl | ⊢ ⦅𝐴, 𝐵⦆ = (⦅𝐴⦆ ∪ ({1o} × tag 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | bj-c2uple 34937 | . 2 class ⦅𝐴, 𝐵⦆ |
4 | 1 | bj-c1upl 34924 | . . 3 class ⦅𝐴⦆ |
5 | c1o 8195 | . . . . 5 class 1o | |
6 | 5 | csn 4541 | . . . 4 class {1o} |
7 | 2 | bj-ctag 34901 | . . . 4 class tag 𝐵 |
8 | 6, 7 | cxp 5549 | . . 3 class ({1o} × tag 𝐵) |
9 | 4, 8 | cun 3864 | . 2 class (⦅𝐴⦆ ∪ ({1o} × tag 𝐵)) |
10 | 3, 9 | wceq 1543 | 1 wff ⦅𝐴, 𝐵⦆ = (⦅𝐴⦆ ∪ ({1o} × tag 𝐵)) |
Colors of variables: wff setvar class |
This definition is referenced by: bj-2upleq 34939 bj-pr21val 34940 bj-pr22val 34946 bj-2uplex 34949 bj-2upln0 34950 bj-2upln1upl 34951 |
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