Description: Lemma for mbfmul . (Contributed by Mario Carneiro, 7-Sep-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mbfmul.1 | |
|
mbfmul.2 | |
||
mbfmul.3 | |
||
mbfmul.4 | |
||
Assertion | mbfmullem | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mbfmul.1 | |
|
2 | mbfmul.2 | |
|
3 | mbfmul.3 | |
|
4 | mbfmul.4 | |
|
5 | 1 3 | mbfi1flim | |
6 | 2 4 | mbfi1flim | |
7 | exdistrv | |
|
8 | 1 | adantr | |
9 | 2 | adantr | |
10 | 3 | adantr | |
11 | 4 | adantr | |
12 | simprll | |
|
13 | simprlr | |
|
14 | fveq2 | |
|
15 | 14 | mpteq2dv | |
16 | fveq2 | |
|
17 | 16 | fveq1d | |
18 | 17 | cbvmptv | |
19 | 15 18 | eqtrdi | |
20 | fveq2 | |
|
21 | 19 20 | breq12d | |
22 | 21 | rspccva | |
23 | 13 22 | sylan | |
24 | simprrl | |
|
25 | simprrr | |
|
26 | fveq2 | |
|
27 | 26 | mpteq2dv | |
28 | fveq2 | |
|
29 | 28 | fveq1d | |
30 | 29 | cbvmptv | |
31 | 27 30 | eqtrdi | |
32 | fveq2 | |
|
33 | 31 32 | breq12d | |
34 | 33 | rspccva | |
35 | 25 34 | sylan | |
36 | 8 9 10 11 12 23 24 35 | mbfmullem2 | |
37 | 36 | ex | |
38 | 37 | exlimdvv | |
39 | 7 38 | syl5bir | |
40 | 5 6 39 | mp2and | |