Step |
Hyp |
Ref |
Expression |
1 |
|
iscmet3.1 |
|
2 |
|
iscmet3.2 |
|
3 |
|
iscmet3.3 |
|
4 |
|
iscmet3.4 |
|
5 |
2
|
cmetcau |
|
6 |
5
|
a1d |
|
7 |
6
|
ralrimiva |
|
8 |
4
|
adantr |
|
9 |
|
simpr |
|
10 |
|
1rp |
|
11 |
|
rphalfcl |
|
12 |
10 11
|
ax-mp |
|
13 |
|
rpexpcl |
|
14 |
12 13
|
mpan |
|
15 |
|
cfili |
|
16 |
9 14 15
|
syl2an |
|
17 |
16
|
ralrimiva |
|
18 |
|
vex |
|
19 |
|
znnen |
|
20 |
|
nnenom |
|
21 |
19 20
|
entri |
|
22 |
|
raleq |
|
23 |
22
|
raleqbi1dv |
|
24 |
18 21 23
|
axcc4 |
|
25 |
17 24
|
syl |
|
26 |
3
|
ad2antrr |
|
27 |
1
|
uzenom |
|
28 |
|
endom |
|
29 |
26 27 28
|
3syl |
|
30 |
|
dfin5 |
|
31 |
|
fzn0 |
|
32 |
31
|
biimpri |
|
33 |
32 1
|
eleq2s |
|
34 |
|
metxmet |
|
35 |
4 34
|
syl |
|
36 |
35
|
adantr |
|
37 |
|
simpl |
|
38 |
|
cfilfil |
|
39 |
36 37 38
|
syl2an |
|
40 |
|
simprr |
|
41 |
|
elfzelz |
|
42 |
|
ffvelrn |
|
43 |
40 41 42
|
syl2an |
|
44 |
|
filelss |
|
45 |
39 43 44
|
syl2an2r |
|
46 |
45
|
ralrimiva |
|
47 |
|
r19.2z |
|
48 |
33 46 47
|
syl2anr |
|
49 |
|
iinss |
|
50 |
48 49
|
syl |
|
51 |
8
|
ad2antrr |
|
52 |
|
elfvdm |
|
53 |
|
fvi |
|
54 |
51 52 53
|
3syl |
|
55 |
50 54
|
sseqtrrd |
|
56 |
|
sseqin2 |
|
57 |
55 56
|
sylib |
|
58 |
30 57
|
syl5eqr |
|
59 |
39
|
adantr |
|
60 |
43
|
ralrimiva |
|
61 |
60
|
adantr |
|
62 |
33
|
adantl |
|
63 |
|
fzfid |
|
64 |
|
iinfi |
|
65 |
59 61 62 63 64
|
syl13anc |
|
66 |
|
filfi |
|
67 |
59 66
|
syl |
|
68 |
65 67
|
eleqtrd |
|
69 |
|
fileln0 |
|
70 |
39 68 69
|
syl2an2r |
|
71 |
58 70
|
eqnetrd |
|
72 |
|
rabn0 |
|
73 |
71 72
|
sylib |
|
74 |
73
|
ralrimiva |
|
75 |
74
|
adantrrr |
|
76 |
|
fvex |
|
77 |
|
eleq1 |
|
78 |
|
fvex |
|
79 |
|
eliin |
|
80 |
78 79
|
ax-mp |
|
81 |
77 80
|
bitrdi |
|
82 |
76 81
|
axcc4dom |
|
83 |
29 75 82
|
syl2anc |
|
84 |
|
df-ral |
|
85 |
|
19.29 |
|
86 |
84 85
|
sylanb |
|
87 |
3
|
ad2antrr |
|
88 |
4
|
ad2antrr |
|
89 |
|
simprrl |
|
90 |
|
feq3 |
|
91 |
88 52 53 90
|
4syl |
|
92 |
89 91
|
mpbid |
|
93 |
|
simplrr |
|
94 |
93
|
simprd |
|
95 |
|
fveq2 |
|
96 |
|
oveq2 |
|
97 |
96
|
breq2d |
|
98 |
95 97
|
raleqbidv |
|
99 |
95 98
|
raleqbidv |
|
100 |
99
|
cbvralvw |
|
101 |
94 100
|
sylib |
|
102 |
|
simprrr |
|
103 |
|
fveq2 |
|
104 |
103
|
eleq2d |
|
105 |
104
|
cbvralvw |
|
106 |
|
oveq2 |
|
107 |
|
fveq2 |
|
108 |
107
|
eleq1d |
|
109 |
106 108
|
raleqbidv |
|
110 |
105 109
|
syl5bb |
|
111 |
110
|
cbvralvw |
|
112 |
102 111
|
sylib |
|
113 |
88 34
|
syl |
|
114 |
|
simplrl |
|
115 |
113 114 38
|
syl2anc |
|
116 |
93
|
simpld |
|
117 |
1 2 87 88 92 101 112
|
iscmet3lem1 |
|
118 |
|
simprl |
|
119 |
117 92 118
|
mp2d |
|
120 |
1 2 87 88 92 101 112 115 116 119
|
iscmet3lem2 |
|
121 |
120
|
ex |
|
122 |
121
|
exlimdv |
|
123 |
86 122
|
syl5 |
|
124 |
123
|
expdimp |
|
125 |
124
|
an32s |
|
126 |
83 125
|
mpd |
|
127 |
126
|
expr |
|
128 |
127
|
exlimdv |
|
129 |
25 128
|
mpd |
|
130 |
129
|
ralrimiva |
|
131 |
2
|
iscmet |
|
132 |
8 130 131
|
sylanbrc |
|
133 |
132
|
ex |
|
134 |
7 133
|
impbid2 |
|