Description: Lemma for 4sq . Sufficient condition to be in S . (Contributed by Mario Carneiro, 14-Jul-2014)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 4sq.1 | |
|
Assertion | 4sqlem3 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4sq.1 | |
|
2 | eqid | |
|
3 | oveq1 | |
|
4 | 3 | oveq1d | |
5 | 4 | oveq2d | |
6 | 5 | eqeq2d | |
7 | oveq1 | |
|
8 | 7 | oveq2d | |
9 | 8 | oveq2d | |
10 | 9 | eqeq2d | |
11 | 6 10 | rspc2ev | |
12 | 2 11 | mp3an3 | |
13 | oveq1 | |
|
14 | 13 | oveq1d | |
15 | 14 | oveq1d | |
16 | 15 | eqeq2d | |
17 | 16 | 2rexbidv | |
18 | oveq1 | |
|
19 | 18 | oveq2d | |
20 | 19 | oveq1d | |
21 | 20 | eqeq2d | |
22 | 21 | 2rexbidv | |
23 | 17 22 | rspc2ev | |
24 | 23 | 3expa | |
25 | 1 | 4sqlem2 | |
26 | 24 25 | sylibr | |
27 | 12 26 | sylan2 | |