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Mathbox for Jeff Madsen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > iscrngo | Structured version Visualization version Unicode version |
Description: The predicate "is a commutative ring". (Contributed by Jeff Madsen, 8-Jun-2010.) |
Ref | Expression |
---|---|
iscrngo |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-crngo 32229 |
. 2
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2 | 1 | elin2 3621 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-v 3047 df-in 3411 df-crngo 32229 |
This theorem is referenced by: iscrngo2 32231 iscringd 32232 crngorngo 32233 fldcrng 32237 isfld2 32238 isdmn2 32288 |
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