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Definition df-nzr 16026
Description: A nonzero or nontrivial ring is a ring with at least two values, or equivalently where 1 and 0 are different. (Contributed by Stefan O'Rear, 24-Feb-2015.)
Assertion
Ref Expression
df-nzr  |- NzRing  =  {
r  e.  Ring  |  ( 1r `  r )  =/=  ( 0g `  r ) }

Detailed syntax breakdown of Definition df-nzr
StepHypRef Expression
1 cnzr 16025 . 2  class NzRing
2 vr . . . . . 6  set  r
32cv 1631 . . . . 5  class  r
4 cur 15355 . . . . 5  class  1r
53, 4cfv 5271 . . . 4  class  ( 1r
`  r )
6 c0g 13416 . . . . 5  class  0g
73, 6cfv 5271 . . . 4  class  ( 0g
`  r )
85, 7wne 2459 . . 3  wff  ( 1r
`  r )  =/=  ( 0g `  r
)
9 crg 15353 . . 3  class  Ring
108, 2, 9crab 2560 . 2  class  { r  e.  Ring  |  ( 1r `  r )  =/=  ( 0g `  r
) }
111, 10wceq 1632 1  wff NzRing  =  {
r  e.  Ring  |  ( 1r `  r )  =/=  ( 0g `  r ) }
Colors of variables: wff set class
This definition is referenced by:  isnzr  16027
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