Description: The predicate "is a commutative monoid". (Contributed by Mario Carneiro, 6-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | iscmn.b | |
|
iscmn.p | |
||
Assertion | iscmn | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iscmn.b | |
|
2 | iscmn.p | |
|
3 | fveq2 | |
|
4 | 3 1 | eqtr4di | |
5 | raleq | |
|
6 | 5 | raleqbi1dv | |
7 | 4 6 | syl | |
8 | fveq2 | |
|
9 | 8 2 | eqtr4di | |
10 | 9 | oveqd | |
11 | 9 | oveqd | |
12 | 10 11 | eqeq12d | |
13 | 12 | 2ralbidv | |
14 | 7 13 | bitrd | |
15 | df-cmn | |
|
16 | 14 15 | elrab2 | |