Step |
Hyp |
Ref |
Expression |
1 |
|
pwssplit4.e |
|
2 |
|
pwssplit4.g |
|
3 |
|
pwssplit4.z |
|
4 |
|
pwssplit4.k |
|
5 |
|
pwssplit4.f |
|
6 |
|
pwssplit4.c |
|
7 |
|
pwssplit4.d |
|
8 |
|
pwssplit4.l |
|
9 |
|
ssrab2 |
|
10 |
4 9
|
eqsstri |
|
11 |
|
resmpt |
|
12 |
10 11
|
ax-mp |
|
13 |
5 12
|
eqtr4i |
|
14 |
|
ssun2 |
|
15 |
14
|
a1i |
|
16 |
|
eqid |
|
17 |
|
eqid |
|
18 |
1 7 2 16 17
|
pwssplit3 |
|
19 |
15 18
|
syld3an3 |
|
20 |
|
simp1 |
|
21 |
|
lmodgrp |
|
22 |
|
grpmnd |
|
23 |
20 21 22
|
3syl |
|
24 |
|
ssun1 |
|
25 |
|
ssexg |
|
26 |
24 25
|
mpan |
|
27 |
26
|
3ad2ant2 |
|
28 |
6 3
|
pws0g |
|
29 |
23 27 28
|
syl2anc |
|
30 |
29
|
eqeq2d |
|
31 |
30
|
rabbidv |
|
32 |
4 31
|
syl5eq |
|
33 |
24
|
a1i |
|
34 |
|
eqid |
|
35 |
|
eqid |
|
36 |
1 6 2 34 35
|
pwssplit3 |
|
37 |
33 36
|
syld3an3 |
|
38 |
|
fvex |
|
39 |
35
|
mptiniseg |
|
40 |
38 39
|
ax-mp |
|
41 |
40
|
eqcomi |
|
42 |
|
eqid |
|
43 |
|
eqid |
|
44 |
41 42 43
|
lmhmkerlss |
|
45 |
37 44
|
syl |
|
46 |
32 45
|
eqeltrd |
|
47 |
43 8
|
reslmhm |
|
48 |
19 46 47
|
syl2anc |
|
49 |
13 48
|
eqeltrid |
|
50 |
5
|
fvtresfn |
|
51 |
|
ssexg |
|
52 |
14 51
|
mpan |
|
53 |
52
|
3ad2ant2 |
|
54 |
7 3
|
pws0g |
|
55 |
23 53 54
|
syl2anc |
|
56 |
55
|
eqcomd |
|
57 |
50 56
|
eqeqan12rd |
|
58 |
|
reseq1 |
|
59 |
58
|
eqeq1d |
|
60 |
59 4
|
elrab2 |
|
61 |
|
uneq12 |
|
62 |
|
resundi |
|
63 |
|
xpundir |
|
64 |
61 62 63
|
3eqtr4g |
|
65 |
64
|
adantll |
|
66 |
65
|
adantl |
|
67 |
|
eqid |
|
68 |
|
simpl1 |
|
69 |
|
simp2 |
|
70 |
69
|
adantr |
|
71 |
|
simprll |
|
72 |
1 67 2 68 70 71
|
pwselbas |
|
73 |
|
ffn |
|
74 |
|
fnresdm |
|
75 |
72 73 74
|
3syl |
|
76 |
1 3
|
pws0g |
|
77 |
23 69 76
|
syl2anc |
|
78 |
1
|
pwslmod |
|
79 |
78
|
3adant3 |
|
80 |
43
|
lsssubg |
|
81 |
79 46 80
|
syl2anc |
|
82 |
|
eqid |
|
83 |
8 82
|
subg0 |
|
84 |
81 83
|
syl |
|
85 |
77 84
|
eqtrd |
|
86 |
85
|
adantr |
|
87 |
66 75 86
|
3eqtr3d |
|
88 |
87
|
exp32 |
|
89 |
60 88
|
syl5bi |
|
90 |
89
|
imp |
|
91 |
57 90
|
sylbid |
|
92 |
91
|
ralrimiva |
|
93 |
|
lmghm |
|
94 |
8 2
|
ressbas2 |
|
95 |
10 94
|
ax-mp |
|
96 |
|
eqid |
|
97 |
|
eqid |
|
98 |
95 16 96 97
|
ghmf1 |
|
99 |
49 93 98
|
3syl |
|
100 |
92 99
|
mpbird |
|
101 |
|
eqid |
|
102 |
101 16
|
lmhmf |
|
103 |
|
frn |
|
104 |
49 102 103
|
3syl |
|
105 |
|
reseq1 |
|
106 |
7 67 16
|
pwselbasb |
|
107 |
20 53 106
|
syl2anc |
|
108 |
107
|
biimpa |
|
109 |
3
|
fvexi |
|
110 |
109
|
fconst |
|
111 |
110
|
a1i |
|
112 |
23
|
adantr |
|
113 |
67 3
|
mndidcl |
|
114 |
112 113
|
syl |
|
115 |
114
|
snssd |
|
116 |
111 115
|
fssd |
|
117 |
|
incom |
|
118 |
|
simp3 |
|
119 |
117 118
|
syl5eq |
|
120 |
119
|
adantr |
|
121 |
|
fun |
|
122 |
108 116 120 121
|
syl21anc |
|
123 |
|
uncom |
|
124 |
|
unidm |
|
125 |
123 124
|
feq23i |
|
126 |
122 125
|
sylib |
|
127 |
1 67 2
|
pwselbasb |
|
128 |
127
|
3adant3 |
|
129 |
128
|
adantr |
|
130 |
126 129
|
mpbird |
|
131 |
|
simpl3 |
|
132 |
117 131
|
syl5eq |
|
133 |
|
ffn |
|
134 |
|
fnresdisj |
|
135 |
108 133 134
|
3syl |
|
136 |
132 135
|
mpbid |
|
137 |
|
fnconstg |
|
138 |
|
fnresdm |
|
139 |
109 137 138
|
mp2b |
|
140 |
139
|
a1i |
|
141 |
136 140
|
uneq12d |
|
142 |
|
resundir |
|
143 |
|
uncom |
|
144 |
|
un0 |
|
145 |
143 144
|
eqtr2i |
|
146 |
141 142 145
|
3eqtr4g |
|
147 |
|
reseq1 |
|
148 |
147
|
eqeq1d |
|
149 |
148 4
|
elrab2 |
|
150 |
130 146 149
|
sylanbrc |
|
151 |
130
|
resexd |
|
152 |
5 105 150 151
|
fvmptd3 |
|
153 |
|
resundir |
|
154 |
|
fnresdm |
|
155 |
108 133 154
|
3syl |
|
156 |
|
ffn |
|
157 |
|
fnresdisj |
|
158 |
110 156 157
|
mp2b |
|
159 |
158
|
biimpi |
|
160 |
159
|
3ad2ant3 |
|
161 |
160
|
adantr |
|
162 |
155 161
|
uneq12d |
|
163 |
|
un0 |
|
164 |
162 163
|
eqtrdi |
|
165 |
153 164
|
syl5eq |
|
166 |
152 165
|
eqtrd |
|
167 |
95 16
|
lmhmf |
|
168 |
|
ffn |
|
169 |
49 167 168
|
3syl |
|
170 |
169
|
adantr |
|
171 |
|
fnfvelrn |
|
172 |
170 150 171
|
syl2anc |
|
173 |
166 172
|
eqeltrrd |
|
174 |
104 173
|
eqelssd |
|
175 |
|
dff1o5 |
|
176 |
100 174 175
|
sylanbrc |
|
177 |
95 16
|
islmim |
|
178 |
49 176 177
|
sylanbrc |
|