Step |
Hyp |
Ref |
Expression |
1 |
|
df-1o |
|
2 |
1
|
fveq2i |
|
3 |
|
peano1 |
|
4 |
|
fmlasuc |
|
5 |
3 4
|
ax-mp |
|
6 |
|
fmla0xp |
|
7 |
|
fmla0 |
|
8 |
7
|
rexeqi |
|
9 |
|
eqeq1 |
|
10 |
9
|
2rexbidv |
|
11 |
10
|
elrab |
|
12 |
|
oveq1 |
|
13 |
12
|
eqeq2d |
|
14 |
13
|
rexbidv |
|
15 |
|
eqidd |
|
16 |
|
id |
|
17 |
15 16
|
goaleq12d |
|
18 |
17
|
eqeq2d |
|
19 |
18
|
rexbidv |
|
20 |
14 19
|
orbi12d |
|
21 |
|
eqeq1 |
|
22 |
21
|
2rexbidv |
|
23 |
|
fmla0 |
|
24 |
22 23
|
elrab2 |
|
25 |
|
oveq2 |
|
26 |
25
|
eqeq2d |
|
27 |
26
|
biimpcd |
|
28 |
27
|
reximdv |
|
29 |
28
|
reximdv |
|
30 |
29
|
com12 |
|
31 |
24 30
|
simplbiim |
|
32 |
31
|
rexlimiv |
|
33 |
32
|
orim1i |
|
34 |
|
r19.43 |
|
35 |
33 34
|
sylibr |
|
36 |
20 35
|
syl6bi |
|
37 |
36
|
com12 |
|
38 |
37
|
reximdv |
|
39 |
38
|
reximdv |
|
40 |
39
|
com12 |
|
41 |
11 40
|
simplbiim |
|
42 |
41
|
rexlimiv |
|
43 |
|
oveq1 |
|
44 |
43
|
oveq1d |
|
45 |
44
|
eqeq2d |
|
46 |
45
|
rexbidv |
|
47 |
|
eqidd |
|
48 |
47 43
|
goaleq12d |
|
49 |
48
|
eqeq2d |
|
50 |
46 49
|
orbi12d |
|
51 |
50
|
rexbidv |
|
52 |
|
oveq2 |
|
53 |
52
|
oveq1d |
|
54 |
53
|
eqeq2d |
|
55 |
54
|
rexbidv |
|
56 |
|
eqidd |
|
57 |
56 52
|
goaleq12d |
|
58 |
57
|
eqeq2d |
|
59 |
55 58
|
orbi12d |
|
60 |
59
|
rexbidv |
|
61 |
51 60
|
cbvrex2vw |
|
62 |
|
oveq1 |
|
63 |
62
|
oveq2d |
|
64 |
63
|
eqeq2d |
|
65 |
64
|
rexbidv |
|
66 |
|
id |
|
67 |
|
eqidd |
|
68 |
66 67
|
goaleq12d |
|
69 |
68
|
eqeq2d |
|
70 |
65 69
|
orbi12d |
|
71 |
70
|
cbvrexvw |
|
72 |
3
|
ne0ii |
|
73 |
|
r19.44zv |
|
74 |
72 73
|
ax-mp |
|
75 |
|
eqeq1 |
|
76 |
75
|
2rexbidv |
|
77 |
|
ovexd |
|
78 |
|
simpl |
|
79 |
43
|
eqeq2d |
|
80 |
79
|
rexbidv |
|
81 |
80
|
adantl |
|
82 |
|
simpr |
|
83 |
52
|
eqeq2d |
|
84 |
83
|
adantl |
|
85 |
|
eqidd |
|
86 |
82 84 85
|
rspcedvd |
|
87 |
78 81 86
|
rspcedvd |
|
88 |
87
|
ad5ant12 |
|
89 |
76 77 88
|
elrabd |
|
90 |
|
oveq1 |
|
91 |
90
|
eqeq2d |
|
92 |
91
|
rexbidv |
|
93 |
|
eqidd |
|
94 |
|
id |
|
95 |
93 94
|
goaleq12d |
|
96 |
95
|
eqeq2d |
|
97 |
96
|
rexbidv |
|
98 |
92 97
|
orbi12d |
|
99 |
98
|
adantl |
|
100 |
|
ovexd |
|
101 |
|
simpr |
|
102 |
101
|
adantr |
|
103 |
|
oveq1 |
|
104 |
103
|
eqeq2d |
|
105 |
104
|
rexbidv |
|
106 |
105
|
adantl |
|
107 |
|
simpr |
|
108 |
|
oveq2 |
|
109 |
108
|
eqeq2d |
|
110 |
109
|
adantl |
|
111 |
|
eqidd |
|
112 |
107 110 111
|
rspcedvd |
|
113 |
102 106 112
|
rspcedvd |
|
114 |
|
eqeq1 |
|
115 |
114
|
2rexbidv |
|
116 |
|
fmla0 |
|
117 |
115 116
|
elrab2 |
|
118 |
100 113 117
|
sylanbrc |
|
119 |
118
|
adantr |
|
120 |
|
oveq2 |
|
121 |
120
|
eqeq2d |
|
122 |
121
|
adantl |
|
123 |
|
simpr |
|
124 |
119 122 123
|
rspcedvd |
|
125 |
124
|
ex |
|
126 |
102
|
adantr |
|
127 |
69
|
adantl |
|
128 |
|
simpr |
|
129 |
126 127 128
|
rspcedvd |
|
130 |
129
|
ex |
|
131 |
125 130
|
orim12d |
|
132 |
131
|
imp |
|
133 |
89 99 132
|
rspcedvd |
|
134 |
133
|
ex |
|
135 |
134
|
rexlimdva |
|
136 |
74 135
|
syl5bir |
|
137 |
136
|
rexlimdva |
|
138 |
71 137
|
syl5bi |
|
139 |
138
|
rexlimivv |
|
140 |
61 139
|
sylbi |
|
141 |
42 140
|
impbii |
|
142 |
8 141
|
bitri |
|
143 |
142
|
abbii |
|
144 |
6 143
|
uneq12i |
|
145 |
2 5 144
|
3eqtri |
|