Step |
Hyp |
Ref |
Expression |
1 |
|
exrecfnlem.1 |
|
2 |
|
rdg0g |
|
3 |
|
peano1 |
|
4 |
|
omelon |
|
5 |
|
limom |
|
6 |
|
rdglimss |
|
7 |
4 5 6
|
mpanl12 |
|
8 |
3 7
|
ax-mp |
|
9 |
2 8
|
eqsstrrdi |
|
10 |
|
rdglim2a |
|
11 |
4 5 10
|
mp2an |
|
12 |
11
|
eleq2i |
|
13 |
|
eliun |
|
14 |
12 13
|
bitri |
|
15 |
|
peano2 |
|
16 |
|
nnon |
|
17 |
|
eqid |
|
18 |
17
|
elrnmpt1 |
|
19 |
|
elun2 |
|
20 |
18 19
|
syl |
|
21 |
|
fvex |
|
22 |
|
nfcv |
|
23 |
|
nfcv |
|
24 |
|
nfmpt1 |
|
25 |
24
|
nfrn |
|
26 |
23 25
|
nfun |
|
27 |
22 26
|
nfmpt |
|
28 |
1 27
|
nfcxfr |
|
29 |
|
nfcv |
|
30 |
28 29
|
nfrdg |
|
31 |
|
nfcv |
|
32 |
30 31
|
nffv |
|
33 |
32
|
mptexgf |
|
34 |
21 33
|
ax-mp |
|
35 |
34
|
rnex |
|
36 |
21 35
|
unex |
|
37 |
|
nfcv |
|
38 |
|
nfcv |
|
39 |
|
nfmpt1 |
|
40 |
1 39
|
nfcxfr |
|
41 |
40 37
|
nfrdg |
|
42 |
41 38
|
nffv |
|
43 |
|
nfcv |
|
44 |
42 43
|
nfmpt |
|
45 |
44
|
nfrn |
|
46 |
42 45
|
nfun |
|
47 |
|
rdgeq1 |
|
48 |
1 47
|
ax-mp |
|
49 |
|
id |
|
50 |
32
|
nfeq2 |
|
51 |
|
eqidd |
|
52 |
50 49 51
|
mpteq12df |
|
53 |
52
|
rneqd |
|
54 |
49 53
|
uneq12d |
|
55 |
37 38 46 48 54
|
rdgsucmptf |
|
56 |
36 55
|
mpan2 |
|
57 |
56
|
eleq2d |
|
58 |
20 57
|
syl5ibr |
|
59 |
16 58
|
syl |
|
60 |
|
rdgellim |
|
61 |
4 5 60
|
mpanl12 |
|
62 |
15 59 61
|
sylsyld |
|
63 |
62
|
expd |
|
64 |
63
|
com3r |
|
65 |
64
|
rexlimdv |
|
66 |
14 65
|
syl5bi |
|
67 |
66
|
alimi |
|
68 |
|
df-ral |
|
69 |
67 68
|
sylibr |
|
70 |
|
fvex |
|
71 |
|
sseq2 |
|
72 |
|
nfcv |
|
73 |
30 72
|
nffv |
|
74 |
73
|
nfeq2 |
|
75 |
|
eleq2 |
|
76 |
|
eleq2 |
|
77 |
75 76
|
imbi12d |
|
78 |
74 77
|
albid |
|
79 |
|
df-ral |
|
80 |
78 79 68
|
3bitr4g |
|
81 |
71 80
|
anbi12d |
|
82 |
70 81
|
spcev |
|
83 |
9 69 82
|
syl2an |
|