Step |
Hyp |
Ref |
Expression |
1 |
|
zssre |
|
2 |
|
sstr |
|
3 |
1 2
|
mpan2 |
|
4 |
|
suprcl |
|
5 |
3 4
|
syl3an1 |
|
6 |
5
|
ltm1d |
|
7 |
|
peano2rem |
|
8 |
4 7
|
syl |
|
9 |
|
suprlub |
|
10 |
8 9
|
mpdan |
|
11 |
3 10
|
syl3an1 |
|
12 |
6 11
|
mpbid |
|
13 |
|
simpl1 |
|
14 |
13
|
sselda |
|
15 |
1 14
|
sseldi |
|
16 |
5
|
adantr |
|
17 |
16
|
adantr |
|
18 |
|
simprl |
|
19 |
13 18
|
sseldd |
|
20 |
|
zre |
|
21 |
19 20
|
syl |
|
22 |
|
peano2re |
|
23 |
21 22
|
syl |
|
24 |
23
|
adantr |
|
25 |
|
suprub |
|
26 |
3 25
|
syl3anl1 |
|
27 |
26
|
adantlr |
|
28 |
|
simprr |
|
29 |
|
1red |
|
30 |
16 29 21
|
ltsubaddd |
|
31 |
28 30
|
mpbid |
|
32 |
31
|
adantr |
|
33 |
15 17 24 27 32
|
lelttrd |
|
34 |
19
|
adantr |
|
35 |
|
zleltp1 |
|
36 |
14 34 35
|
syl2anc |
|
37 |
33 36
|
mpbird |
|
38 |
37
|
ralrimiva |
|
39 |
|
suprleub |
|
40 |
3 39
|
syl3anl1 |
|
41 |
21 40
|
syldan |
|
42 |
38 41
|
mpbird |
|
43 |
|
suprub |
|
44 |
3 43
|
syl3anl1 |
|
45 |
44
|
adantrr |
|
46 |
16 21
|
letri3d |
|
47 |
42 45 46
|
mpbir2and |
|
48 |
47 18
|
eqeltrd |
|
49 |
12 48
|
rexlimddv |
|