Step |
Hyp |
Ref |
Expression |
1 |
|
zex |
|
2 |
|
difexg |
|
3 |
1 2
|
ax-mp |
|
4 |
|
ominf |
|
5 |
|
nnuz |
|
6 |
|
0p1e1 |
|
7 |
6
|
fveq2i |
|
8 |
5 7
|
eqtr4i |
|
9 |
8
|
difeq2i |
|
10 |
|
0z |
|
11 |
|
lzenom |
|
12 |
10 11
|
ax-mp |
|
13 |
9 12
|
eqbrtri |
|
14 |
|
enfi |
|
15 |
13 14
|
ax-mp |
|
16 |
4 15
|
mtbir |
|
17 |
|
incom |
|
18 |
|
disjdif |
|
19 |
17 18
|
eqtri |
|
20 |
3 16 19
|
eldioph4b |
|
21 |
|
simpr |
|
22 |
|
simp-4r |
|
23 |
|
ovex |
|
24 |
23
|
mapco2 |
|
25 |
21 22 24
|
syl2anc |
|
26 |
|
uneq1 |
|
27 |
26
|
fveqeq2d |
|
28 |
27
|
rexbidv |
|
29 |
28
|
elrab3 |
|
30 |
25 29
|
syl |
|
31 |
|
simp-5r |
|
32 |
|
simplr |
|
33 |
|
simpr |
|
34 |
|
coundi |
|
35 |
|
coundir |
|
36 |
|
elmapi |
|
37 |
36
|
3ad2ant3 |
|
38 |
|
simp1 |
|
39 |
|
incom |
|
40 |
|
fz1ssnn |
|
41 |
|
ssdisj |
|
42 |
40 18 41
|
mp2an |
|
43 |
39 42
|
eqtri |
|
44 |
43
|
a1i |
|
45 |
|
coeq0i |
|
46 |
37 38 44 45
|
syl3anc |
|
47 |
46
|
uneq2d |
|
48 |
35 47
|
syl5eq |
|
49 |
|
un0 |
|
50 |
48 49
|
eqtrdi |
|
51 |
|
coundir |
|
52 |
|
elmapi |
|
53 |
52
|
3ad2ant2 |
|
54 |
|
f1oi |
|
55 |
|
f1of |
|
56 |
54 55
|
ax-mp |
|
57 |
|
coeq0i |
|
58 |
56 42 57
|
mp3an23 |
|
59 |
53 58
|
syl |
|
60 |
|
coires1 |
|
61 |
|
ffn |
|
62 |
|
fnresdm |
|
63 |
36 61 62
|
3syl |
|
64 |
60 63
|
syl5eq |
|
65 |
64
|
3ad2ant3 |
|
66 |
59 65
|
uneq12d |
|
67 |
51 66
|
syl5eq |
|
68 |
|
uncom |
|
69 |
|
un0 |
|
70 |
68 69
|
eqtri |
|
71 |
67 70
|
eqtrdi |
|
72 |
50 71
|
uneq12d |
|
73 |
34 72
|
syl5req |
|
74 |
31 32 33 73
|
syl3anc |
|
75 |
74
|
fveq2d |
|
76 |
|
nn0ssz |
|
77 |
|
mapss |
|
78 |
1 76 77
|
mp2an |
|
79 |
42
|
reseq2i |
|
80 |
|
res0 |
|
81 |
79 80
|
eqtri |
|
82 |
42
|
reseq2i |
|
83 |
|
res0 |
|
84 |
82 83
|
eqtri |
|
85 |
81 84
|
eqtr4i |
|
86 |
|
elmapresaun |
|
87 |
|
uncom |
|
88 |
87
|
oveq2i |
|
89 |
86 88
|
eleqtrdi |
|
90 |
85 89
|
mp3an3 |
|
91 |
78 90
|
sseldi |
|
92 |
91
|
adantll |
|
93 |
|
coeq1 |
|
94 |
93
|
fveq2d |
|
95 |
|
eqid |
|
96 |
|
fvex |
|
97 |
94 95 96
|
fvmpt |
|
98 |
92 97
|
syl |
|
99 |
75 98
|
eqtr4d |
|
100 |
99
|
eqeq1d |
|
101 |
100
|
rexbidva |
|
102 |
30 101
|
bitrd |
|
103 |
102
|
rabbidva |
|
104 |
|
simplll |
|
105 |
|
ovex |
|
106 |
3 105
|
unex |
|
107 |
106
|
a1i |
|
108 |
|
simpr |
|
109 |
56
|
a1i |
|
110 |
|
id |
|
111 |
|
incom |
|
112 |
|
fz1ssnn |
|
113 |
|
ssdisj |
|
114 |
112 18 113
|
mp2an |
|
115 |
111 114
|
eqtri |
|
116 |
115
|
a1i |
|
117 |
|
fun |
|
118 |
109 110 116 117
|
syl21anc |
|
119 |
|
uncom |
|
120 |
119
|
feq1i |
|
121 |
118 120
|
sylib |
|
122 |
121
|
ad3antlr |
|
123 |
|
mzprename |
|
124 |
107 108 122 123
|
syl3anc |
|
125 |
3 16 19
|
eldioph4i |
|
126 |
104 124 125
|
syl2anc |
|
127 |
103 126
|
eqeltrd |
|
128 |
|
eleq2 |
|
129 |
128
|
rabbidv |
|
130 |
129
|
eleq1d |
|
131 |
127 130
|
syl5ibrcom |
|
132 |
131
|
rexlimdva |
|
133 |
132
|
expimpd |
|
134 |
20 133
|
syl5bi |
|
135 |
134
|
impcom |
|
136 |
135
|
3impb |
|