Description: Swap the arguments of the trace of a composition with converse. (Contributed by NM, 1-Jul-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | trlcocnv.h | |
|
trlcocnv.t | |
||
trlcocnv.r | |
||
Assertion | trlcocnv | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | trlcocnv.h | |
|
2 | trlcocnv.t | |
|
3 | trlcocnv.r | |
|
4 | simp1 | |
|
5 | 1 2 | ltrncnv | |
6 | 5 | 3adant2 | |
7 | 1 2 | ltrnco | |
8 | 6 7 | syld3an3 | |
9 | 1 2 3 | trlcnv | |
10 | 4 8 9 | syl2anc | |
11 | cnvco | |
|
12 | cocnvcnv1 | |
|
13 | 11 12 | eqtri | |
14 | 13 | fveq2i | |
15 | 10 14 | eqtr3di | |