Step |
Hyp |
Ref |
Expression |
1 |
|
prdscmnd.y |
|
2 |
|
prdscmnd.i |
|
3 |
|
prdscmnd.s |
|
4 |
|
prdscmnd.r |
|
5 |
|
eqidd |
|
6 |
|
eqidd |
|
7 |
|
cmnmnd |
|
8 |
7
|
ssriv |
|
9 |
|
fss |
|
10 |
4 8 9
|
sylancl |
|
11 |
1 2 3 10
|
prdsmndd |
|
12 |
4
|
3ad2ant1 |
|
13 |
12
|
ffvelrnda |
|
14 |
|
eqid |
|
15 |
3
|
elexd |
|
16 |
15
|
3ad2ant1 |
|
17 |
16
|
adantr |
|
18 |
2
|
elexd |
|
19 |
18
|
3ad2ant1 |
|
20 |
19
|
adantr |
|
21 |
4
|
ffnd |
|
22 |
21
|
3ad2ant1 |
|
23 |
22
|
adantr |
|
24 |
|
simpl2 |
|
25 |
|
simpr |
|
26 |
1 14 17 20 23 24 25
|
prdsbasprj |
|
27 |
|
simpl3 |
|
28 |
1 14 17 20 23 27 25
|
prdsbasprj |
|
29 |
|
eqid |
|
30 |
|
eqid |
|
31 |
29 30
|
cmncom |
|
32 |
13 26 28 31
|
syl3anc |
|
33 |
32
|
mpteq2dva |
|
34 |
|
simp2 |
|
35 |
|
simp3 |
|
36 |
|
eqid |
|
37 |
1 14 16 19 22 34 35 36
|
prdsplusgval |
|
38 |
1 14 16 19 22 35 34 36
|
prdsplusgval |
|
39 |
33 37 38
|
3eqtr4d |
|
40 |
5 6 11 39
|
iscmnd |
|