Step |
Hyp |
Ref |
Expression |
1 |
|
0cn |
|
2 |
|
ifcl |
|
3 |
1 2
|
mpan2 |
|
4 |
3
|
ad2antrr |
|
5 |
|
simpll |
|
6 |
4 5 5
|
add12d |
|
7 |
5 4 5
|
addassd |
|
8 |
6 7
|
eqtr4d |
|
9 |
|
pm5.501 |
|
10 |
9
|
adantl |
|
11 |
10
|
bicomd |
|
12 |
11
|
ifbid |
|
13 |
|
animorrl |
|
14 |
|
iftrue |
|
15 |
13 14
|
syl |
|
16 |
5
|
2timesd |
|
17 |
15 16
|
eqtrd |
|
18 |
12 17
|
oveq12d |
|
19 |
|
iftrue |
|
20 |
19
|
adantl |
|
21 |
20
|
oveq1d |
|
22 |
21
|
oveq1d |
|
23 |
8 18 22
|
3eqtr4d |
|
24 |
|
iffalse |
|
25 |
24
|
adantl |
|
26 |
25
|
oveq1d |
|
27 |
3
|
ad2antrr |
|
28 |
27
|
addid2d |
|
29 |
26 28
|
eqtrd |
|
30 |
29
|
oveq1d |
|
31 |
|
2cnd |
|
32 |
|
id |
|
33 |
31 32
|
mulcld |
|
34 |
33
|
addid2d |
|
35 |
|
2times |
|
36 |
34 35
|
eqtrd |
|
37 |
36
|
adantr |
|
38 |
|
iftrue |
|
39 |
38
|
adantl |
|
40 |
|
iftrue |
|
41 |
40
|
adantl |
|
42 |
39 41
|
oveq12d |
|
43 |
|
iftrue |
|
44 |
43
|
adantl |
|
45 |
44
|
oveq1d |
|
46 |
37 42 45
|
3eqtr4d |
|
47 |
|
simpl |
|
48 |
|
0cnd |
|
49 |
47 48
|
addcomd |
|
50 |
|
iffalse |
|
51 |
50
|
adantl |
|
52 |
|
iffalse |
|
53 |
52
|
adantl |
|
54 |
51 53
|
oveq12d |
|
55 |
|
iffalse |
|
56 |
55
|
adantl |
|
57 |
56
|
oveq1d |
|
58 |
49 54 57
|
3eqtr4d |
|
59 |
46 58
|
pm2.61dan |
|
60 |
59
|
ad2antrr |
|
61 |
|
ifnot |
|
62 |
|
nbn2 |
|
63 |
62
|
adantl |
|
64 |
63
|
ifbid |
|
65 |
61 64
|
syl5eqr |
|
66 |
|
biorf |
|
67 |
66
|
adantl |
|
68 |
67
|
ifbid |
|
69 |
65 68
|
oveq12d |
|
70 |
30 60 69
|
3eqtr2rd |
|
71 |
23 70
|
pm2.61dan |
|
72 |
|
hadrot |
|
73 |
|
had1 |
|
74 |
72 73
|
bitr3id |
|
75 |
74
|
adantl |
|
76 |
75
|
ifbid |
|
77 |
|
cad1 |
|
78 |
77
|
adantl |
|
79 |
78
|
ifbid |
|
80 |
76 79
|
oveq12d |
|
81 |
|
iftrue |
|
82 |
81
|
adantl |
|
83 |
82
|
oveq2d |
|
84 |
71 80 83
|
3eqtr4d |
|
85 |
19
|
adantl |
|
86 |
85
|
oveq1d |
|
87 |
44
|
oveq2d |
|
88 |
37 42 87
|
3eqtr4d |
|
89 |
53 56
|
eqtr4d |
|
90 |
51 89
|
oveq12d |
|
91 |
88 90
|
pm2.61dan |
|
92 |
91
|
ad2antrr |
|
93 |
9
|
adantl |
|
94 |
93
|
notbid |
|
95 |
|
df-xor |
|
96 |
94 95
|
bitr4di |
|
97 |
96
|
ifbid |
|
98 |
61 97
|
syl5eqr |
|
99 |
|
ibar |
|
100 |
99
|
adantl |
|
101 |
100
|
ifbid |
|
102 |
98 101
|
oveq12d |
|
103 |
86 92 102
|
3eqtr2rd |
|
104 |
|
simplll |
|
105 |
|
0cnd |
|
106 |
104 105
|
ifclda |
|
107 |
|
0cnd |
|
108 |
106 107
|
addcomd |
|
109 |
62
|
adantl |
|
110 |
109
|
con1bid |
|
111 |
95 110
|
syl5bb |
|
112 |
111
|
ifbid |
|
113 |
|
simpr |
|
114 |
113
|
intnanrd |
|
115 |
|
iffalse |
|
116 |
114 115
|
syl |
|
117 |
112 116
|
oveq12d |
|
118 |
24
|
adantl |
|
119 |
118
|
oveq1d |
|
120 |
108 117 119
|
3eqtr4d |
|
121 |
103 120
|
pm2.61dan |
|
122 |
|
had0 |
|
123 |
72 122
|
bitr3id |
|
124 |
123
|
adantl |
|
125 |
124
|
ifbid |
|
126 |
|
cad0 |
|
127 |
126
|
adantl |
|
128 |
127
|
ifbid |
|
129 |
125 128
|
oveq12d |
|
130 |
|
iffalse |
|
131 |
130
|
oveq2d |
|
132 |
|
ifcl |
|
133 |
1 132
|
mpan2 |
|
134 |
133 3
|
addcld |
|
135 |
134
|
addid1d |
|
136 |
131 135
|
sylan9eqr |
|
137 |
121 129 136
|
3eqtr4d |
|
138 |
84 137
|
pm2.61dan |
|