Description: The join of a poset is commutative. (This may not be a theorem under other definitions of meet.) (Contributed by NM, 16-Sep-2011) (New usage is discouraged.) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | joincom.b | |
|
joincom.j | |
||
Assertion | joincomALT | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | joincom.b | |
|
2 | joincom.j | |
|
3 | prcom | |
|
4 | 3 | fveq2i | |
5 | 4 | a1i | |
6 | eqid | |
|
7 | simp1 | |
|
8 | simp3 | |
|
9 | simp2 | |
|
10 | 6 2 7 8 9 | joinval | |
11 | 6 2 7 9 8 | joinval | |
12 | 5 10 11 | 3eqtr4rd | |