|   | Mathbox for BJ | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-pr1 | Structured version Visualization version GIF version | ||
| Description: Definition of the first projection of a class tuple. New usage is discouraged because the precise definition is generally unimportant compared to the characteristic properties bj-pr1eq 37004, bj-pr11val 37007, bj-pr21val 37015, bj-pr1ex 37008. (Contributed by BJ, 6-Apr-2019.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| df-bj-pr1 | ⊢ pr1 𝐴 = (∅ Proj 𝐴) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | cA | . . 3 class 𝐴 | |
| 2 | 1 | bj-cpr1 37002 | . 2 class pr1 𝐴 | 
| 3 | c0 4332 | . . 3 class ∅ | |
| 4 | 3, 1 | bj-cproj 36992 | . 2 class (∅ Proj 𝐴) | 
| 5 | 2, 4 | wceq 1539 | 1 wff pr1 𝐴 = (∅ Proj 𝐴) | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: bj-pr1eq 37004 bj-pr1un 37005 bj-pr1val 37006 bj-pr1ex 37008 | 
| Copyright terms: Public domain | W3C validator |