![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-diagval2 | Structured version Visualization version GIF version |
Description: Value of the functionalized identity, or equivalently of the diagonal function. This expression views it as the diagonal function, whereas bj-diagval 37117 views it as the functionalized identity. See df-bj-diag 37116 for the terminology. (Contributed by BJ, 22-Jun-2019.) |
Ref | Expression |
---|---|
bj-diagval2 | ⊢ (𝐴 ∈ 𝑉 → (Id‘𝐴) = ( I ∩ (𝐴 × 𝐴))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-diagval 37117 | . 2 ⊢ (𝐴 ∈ 𝑉 → (Id‘𝐴) = ( I ↾ 𝐴)) | |
2 | idinxpresid 6063 | . 2 ⊢ ( I ∩ (𝐴 × 𝐴)) = ( I ↾ 𝐴) | |
3 | 1, 2 | eqtr4di 2791 | 1 ⊢ (𝐴 ∈ 𝑉 → (Id‘𝐴) = ( I ∩ (𝐴 × 𝐴))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1535 ∈ wcel 2104 ∩ cin 3962 I cid 5576 × cxp 5682 ↾ cres 5686 ‘cfv 6559 Idcdiag2 37115 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1963 ax-7 2003 ax-8 2106 ax-9 2114 ax-10 2137 ax-11 2153 ax-12 2173 ax-ext 2704 ax-sep 5301 ax-nul 5308 ax-pow 5367 ax-pr 5431 ax-un 7748 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-3an 1087 df-tru 1538 df-fal 1548 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2536 df-eu 2565 df-clab 2711 df-cleq 2725 df-clel 2812 df-nfc 2888 df-ral 3058 df-rex 3067 df-rab 3433 df-v 3479 df-dif 3966 df-un 3968 df-in 3970 df-ss 3980 df-nul 4340 df-if 4532 df-pw 4607 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4916 df-br 5151 df-opab 5213 df-mpt 5234 df-id 5577 df-xp 5690 df-rel 5691 df-cnv 5692 df-co 5693 df-dm 5694 df-res 5696 df-iota 6511 df-fun 6561 df-fv 6567 df-bj-diag 37116 |
This theorem is referenced by: bj-eldiag 37119 bj-eldiag2 37120 |
Copyright terms: Public domain | W3C validator |