![]() |
Mathbox for Jeff Madsen |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > isdmn | Structured version Visualization version GIF version |
Description: The predicate "is a domain". (Contributed by Jeff Madsen, 10-Jun-2010.) |
Ref | Expression |
---|---|
isdmn | ⊢ (𝑅 ∈ Dmn ↔ (𝑅 ∈ PrRing ∧ 𝑅 ∈ Com2)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dmn 36497 | . 2 ⊢ Dmn = (PrRing ∩ Com2) | |
2 | 1 | elin2 4156 | 1 ⊢ (𝑅 ∈ Dmn ↔ (𝑅 ∈ PrRing ∧ 𝑅 ∈ Com2)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 396 ∈ wcel 2106 Com2ccm2 36437 PrRingcprrng 36494 Dmncdmn 36495 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3446 df-in 3916 df-dmn 36497 |
This theorem is referenced by: isdmn2 36503 |
Copyright terms: Public domain | W3C validator |