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Definition df-bj-proj 32954
Description: Definition of the class projection corresponding to tagged tuples. The expression (𝐴 Proj 𝐵) denotes the projection on the A^th component. (Contributed by BJ, 6-Apr-2019.) (New usage is discouraged.)
Assertion
Ref Expression
df-bj-proj (𝐴 Proj 𝐵) = {𝑥 ∣ {𝑥} ∈ (𝐵 “ {𝐴})}
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵

Detailed syntax breakdown of Definition df-bj-proj
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2bj-cproj 32953 . 2 class (𝐴 Proj 𝐵)
4 vx . . . . . 6 setvar 𝑥
54cv 1480 . . . . 5 class 𝑥
65csn 4168 . . . 4 class {𝑥}
71csn 4168 . . . . 5 class {𝐴}
82, 7cima 5107 . . . 4 class (𝐵 “ {𝐴})
96, 8wcel 1988 . . 3 wff {𝑥} ∈ (𝐵 “ {𝐴})
109, 4cab 2606 . 2 class {𝑥 ∣ {𝑥} ∈ (𝐵 “ {𝐴})}
113, 10wceq 1481 1 wff (𝐴 Proj 𝐵) = {𝑥 ∣ {𝑥} ∈ (𝐵 “ {𝐴})}
Colors of variables: wff setvar class
This definition is referenced by:  bj-projeq  32955  bj-projun  32957  bj-projex  32958  bj-projval  32959
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