Description: Weak order condition of the inclusion poset. (Contributed by Stefan O'Rear, 30-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ipoval.i | |
|
ipole.l | |
||
Assertion | ipole | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ipoval.i | |
|
2 | ipole.l | |
|
3 | preq12 | |
|
4 | 3 | sseq1d | |
5 | sseq12 | |
|
6 | 4 5 | anbi12d | |
7 | eqid | |
|
8 | 6 7 | brabga | |
9 | 8 | 3adant1 | |
10 | 1 | ipolerval | |
11 | 2 10 | eqtr4id | |
12 | 11 | breqd | |
13 | 12 | 3ad2ant1 | |
14 | prssi | |
|
15 | 14 | 3adant1 | |
16 | 15 | biantrurd | |
17 | 9 13 16 | 3bitr4d | |