Description: Converse of qustriv . (Contributed by Thierry Arnoux, 15-Jan-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | qustrivr.1 | |
|
qustrivr.2 | |
||
Assertion | qustrivr | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qustrivr.1 | |
|
2 | qustrivr.2 | |
|
3 | 2 | a1i | |
4 | 1 | a1i | |
5 | ovexd | |
|
6 | simpl | |
|
7 | 3 4 5 6 | qusbas | |
8 | 7 | 3adant3 | |
9 | simp3 | |
|
10 | 8 9 | eqtrd | |
11 | 10 | unieqd | |
12 | eqid | |
|
13 | 1 12 | eqger | |
14 | 13 | adantl | |
15 | 14 5 | uniqs2 | |
16 | 15 | 3adant3 | |
17 | unisng | |
|
18 | 17 | 3ad2ant2 | |
19 | 11 16 18 | 3eqtr3rd | |