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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 36999. New usage is discouraged because the precise definition is generally unimportant compared to the characteristic properties bj-2upleq 37013, bj-2uplth 37022, bj-2uplex 37023, and the properties of the projections (see df-bj-pr1 37002 and df-bj-pr2 37016). (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 37011 | . 2 class ⦅𝐴, 𝐵⦆ | 
| 4 | 1 | bj-c1upl 36998 | . . 3 class ⦅𝐴⦆ | 
| 5 | c1o 8499 | . . . . 5 class 1o | |
| 6 | 5 | csn 4626 | . . . 4 class {1o} | 
| 7 | 2 | bj-ctag 36975 | . . . 4 class tag 𝐵 | 
| 8 | 6, 7 | cxp 5683 | . . 3 class ({1o} × tag 𝐵) | 
| 9 | 4, 8 | cun 3949 | . 2 class (⦅𝐴⦆ ∪ ({1o} × tag 𝐵)) | 
| 10 | 3, 9 | wceq 1540 | 1 wff ⦅𝐴, 𝐵⦆ = (⦅𝐴⦆ ∪ ({1o} × tag 𝐵)) | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: bj-2upleq 37013 bj-pr21val 37014 bj-pr22val 37020 bj-2uplex 37023 bj-2upln0 37024 bj-2upln1upl 37025 | 
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