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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 34207. New usage is discouraged because the precise definition is generally unimportant compared to the characteristic properties bj-2upleq 34221, bj-2uplth 34230, bj-2uplex 34231, and the properties of the projections (see df-bj-pr1 34210 and df-bj-pr2 34224). (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 34219 | . 2 class ⦅𝐴, 𝐵⦆ |
4 | 1 | bj-c1upl 34206 | . . 3 class ⦅𝐴⦆ |
5 | c1o 8084 | . . . . 5 class 1o | |
6 | 5 | csn 4557 | . . . 4 class {1o} |
7 | 2 | bj-ctag 34183 | . . . 4 class tag 𝐵 |
8 | 6, 7 | cxp 5546 | . . 3 class ({1o} × tag 𝐵) |
9 | 4, 8 | cun 3931 | . 2 class (⦅𝐴⦆ ∪ ({1o} × tag 𝐵)) |
10 | 3, 9 | wceq 1528 | 1 wff ⦅𝐴, 𝐵⦆ = (⦅𝐴⦆ ∪ ({1o} × tag 𝐵)) |
Colors of variables: wff setvar class |
This definition is referenced by: bj-2upleq 34221 bj-pr21val 34222 bj-pr22val 34228 bj-2uplex 34231 bj-2upln0 34232 bj-2upln1upl 34233 |
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