Step | Hyp | Ref
| Expression |
1 | | ncaddccl 6144 |
. . . 4
NC NC NC |
2 | | ce0nnul 6177 |
. . . . 5
NC
↑c 0c
1 |
3 | | eladdc 4398 |
. . . . . 6
1
1 |
4 | 3 | exbii 1582 |
. . . . 5
1
1 |
5 | 2, 4 | syl6bb 252 |
. . . 4
NC
↑c 0c
1 |
6 | 1, 5 | syl 15 |
. . 3
NC NC ↑c 0c 1 |
7 | | ncseqnc 6128 |
. . . . . . . 8
NC Nc |
8 | | ncseqnc 6128 |
. . . . . . . 8
NC Nc |
9 | 7, 8 | bi2anan9 843 |
. . . . . . 7
NC NC Nc Nc
|
10 | 9 | biimpar 471 |
. . . . . 6
NC NC
Nc Nc |
11 | | ssun1 3426 |
. . . . . . . . . . . 12
|
12 | | id 19 |
. . . . . . . . . . . 12
1
1 |
13 | 11, 12 | syl5sseqr 3320 |
. . . . . . . . . . 11
1
1 |
14 | | ssun2 3427 |
. . . . . . . . . . . 12
|
15 | 14, 12 | syl5sseqr 3320 |
. . . . . . . . . . 11
1
1 |
16 | 13, 15 | jca 518 |
. . . . . . . . . 10
1
1
1 |
17 | | vex 2862 |
. . . . . . . . . . . . 13
|
18 | 17 | sspw1 4335 |
. . . . . . . . . . . 12
1
1 |
19 | | vex 2862 |
. . . . . . . . . . . . 13
|
20 | 19 | sspw1 4335 |
. . . . . . . . . . . 12
1
1 |
21 | 18, 20 | anbi12i 678 |
. . . . . . . . . . 11
1 1
1
1 |
22 | | eeanv 1913 |
. . . . . . . . . . 11
1
1
1
1 |
23 | 21, 22 | bitr4i 243 |
. . . . . . . . . 10
1 1
1 1 |
24 | 16, 23 | sylib 188 |
. . . . . . . . 9
1
1
1 |
25 | | pw1eq 4143 |
. . . . . . . . . . . . . . . . 17
1 1 |
26 | 25 | eleq1d 2419 |
. . . . . . . . . . . . . . . 16
1 Nc 1 1 Nc 1 |
27 | | vex 2862 |
. . . . . . . . . . . . . . . . . 18
|
28 | 27 | pw1ex 4303 |
. . . . . . . . . . . . . . . . 17
1 |
29 | 28 | ncid 6123 |
. . . . . . . . . . . . . . . 16
1 Nc 1 |
30 | 26, 29 | speiv 2000 |
. . . . . . . . . . . . . . 15
1 Nc 1 |
31 | | ncelncs 6120 |
. . . . . . . . . . . . . . . 16
1 Nc 1 NC |
32 | | ce0nnul 6177 |
. . . . . . . . . . . . . . . 16
Nc 1 NC Nc 1 ↑c 0c 1
Nc 1 |
33 | 28, 31, 32 | mp2b 9 |
. . . . . . . . . . . . . . 15
Nc 1 ↑c
0c
1 Nc 1 |
34 | 30, 33 | mpbir 200 |
. . . . . . . . . . . . . 14
Nc 1 ↑c 0c |
35 | | pw1eq 4143 |
. . . . . . . . . . . . . . . . 17
1 1 |
36 | 35 | eleq1d 2419 |
. . . . . . . . . . . . . . . 16
1 Nc 1
1 Nc 1 |
37 | | vex 2862 |
. . . . . . . . . . . . . . . . . 18
|
38 | 37 | pw1ex 4303 |
. . . . . . . . . . . . . . . . 17
1 |
39 | 38 | ncid 6123 |
. . . . . . . . . . . . . . . 16
1 Nc 1 |
40 | 36, 39 | speiv 2000 |
. . . . . . . . . . . . . . 15
1 Nc 1 |
41 | | ncelncs 6120 |
. . . . . . . . . . . . . . . 16
1
Nc
1 NC |
42 | | ce0nnul 6177 |
. . . . . . . . . . . . . . . 16
Nc 1
NC Nc 1
↑c 0c
1 Nc 1 |
43 | 38, 41, 42 | mp2b 9 |
. . . . . . . . . . . . . . 15
Nc 1 ↑c
0c
1 Nc 1 |
44 | 40, 43 | mpbir 200 |
. . . . . . . . . . . . . 14
Nc 1
↑c 0c |
45 | 34, 44 | pm3.2i 441 |
. . . . . . . . . . . . 13
Nc 1 ↑c
0c
Nc 1 ↑c
0c
|
46 | | nceq 6108 |
. . . . . . . . . . . . . . . 16
1 Nc Nc 1 |
47 | 46 | oveq1d 5537 |
. . . . . . . . . . . . . . 15
1 Nc ↑c 0c
Nc 1 ↑c 0c |
48 | 47 | neeq1d 2529 |
. . . . . . . . . . . . . 14
1 Nc ↑c
0c
Nc 1 ↑c 0c |
49 | | nceq 6108 |
. . . . . . . . . . . . . . . 16
1
Nc Nc 1 |
50 | 49 | oveq1d 5537 |
. . . . . . . . . . . . . . 15
1
Nc ↑c
0c
Nc 1 ↑c
0c |
51 | 50 | neeq1d 2529 |
. . . . . . . . . . . . . 14
1
Nc ↑c
0c
Nc 1
↑c 0c |
52 | 48, 51 | bi2anan9 843 |
. . . . . . . . . . . . 13
1
1 Nc ↑c 0c Nc ↑c 0c Nc 1 ↑c
0c
Nc 1 ↑c
0c
|
53 | 45, 52 | mpbiri 224 |
. . . . . . . . . . . 12
1
1 Nc ↑c 0c Nc ↑c 0c |
54 | 53 | ad2ant2l 726 |
. . . . . . . . . . 11
1
1
Nc ↑c 0c Nc ↑c 0c |
55 | 54 | a1d 22 |
. . . . . . . . . 10
1
1
Nc ↑c
0c
Nc ↑c
0c
|
56 | 55 | exlimivv 1635 |
. . . . . . . . 9
1
1
Nc ↑c
0c
Nc ↑c
0c
|
57 | 24, 56 | syl 15 |
. . . . . . . 8
1
Nc ↑c
0c
Nc ↑c
0c
|
58 | 57 | impcom 419 |
. . . . . . 7
1
Nc ↑c 0c Nc ↑c 0c |
59 | | oveq1 5530 |
. . . . . . . . 9
Nc ↑c
0c
Nc ↑c
0c |
60 | 59 | neeq1d 2529 |
. . . . . . . 8
Nc ↑c
0c
Nc ↑c 0c |
61 | | oveq1 5530 |
. . . . . . . . 9
Nc ↑c
0c
Nc ↑c
0c |
62 | 61 | neeq1d 2529 |
. . . . . . . 8
Nc ↑c
0c
Nc ↑c 0c |
63 | 60, 62 | bi2anan9 843 |
. . . . . . 7
Nc Nc ↑c
0c
↑c 0c
Nc ↑c
0c
Nc ↑c
0c
|
64 | 58, 63 | syl5ibr 212 |
. . . . . 6
Nc Nc 1 ↑c
0c
↑c 0c |
65 | 10, 64 | syl 15 |
. . . . 5
NC NC 1 ↑c
0c
↑c 0c |
66 | 65 | rexlimdvva 2745 |
. . . 4
NC NC
1 ↑c
0c
↑c 0c |
67 | 66 | exlimdv 1636 |
. . 3
NC NC
1
↑c 0c
↑c 0c |
68 | 6, 67 | sylbid 206 |
. 2
NC NC ↑c 0c ↑c
0c
↑c 0c |
69 | | ce0nnul 6177 |
. . . . 5
NC ↑c
0c
1 |
70 | | ce0nnul 6177 |
. . . . 5
NC ↑c
0c
1 |
71 | 69, 70 | bi2anan9 843 |
. . . 4
NC NC
↑c 0c
↑c 0c
1
1 |
72 | | eeanv 1913 |
. . . 4
1
1 1
1
|
73 | 71, 72 | syl6bbr 254 |
. . 3
NC NC
↑c 0c
↑c 0c
1 1 |
74 | | ncseqnc 6128 |
. . . . . 6
NC Nc 1
1 |
75 | | ncseqnc 6128 |
. . . . . 6
NC Nc 1
1 |
76 | 74, 75 | bi2anan9 843 |
. . . . 5
NC NC Nc 1
Nc 1 1
1
|
77 | | vvex 4109 |
. . . . . . . . . . . 12
|
78 | 17, 77 | xpsnen 6049 |
. . . . . . . . . . 11
|
79 | | enpw1 6062 |
. . . . . . . . . . 11
1 1 |
80 | 78, 79 | mpbi 199 |
. . . . . . . . . 10
1 1 |
81 | | snex 4111 |
. . . . . . . . . . . . 13
|
82 | 17, 81 | xpex 5115 |
. . . . . . . . . . . 12
|
83 | 82 | pw1ex 4303 |
. . . . . . . . . . 11
1 |
84 | 83 | eqnc 6127 |
. . . . . . . . . 10
Nc 1 Nc 1
1 1 |
85 | 80, 84 | mpbir 200 |
. . . . . . . . 9
Nc 1 Nc 1 |
86 | | 0ex 4110 |
. . . . . . . . . . . 12
|
87 | 19, 86 | xpsnen 6049 |
. . . . . . . . . . 11
|
88 | | enpw1 6062 |
. . . . . . . . . . 11
1 1 |
89 | 87, 88 | mpbi 199 |
. . . . . . . . . 10
1 1 |
90 | | snex 4111 |
. . . . . . . . . . . . 13
|
91 | 19, 90 | xpex 5115 |
. . . . . . . . . . . 12
|
92 | 91 | pw1ex 4303 |
. . . . . . . . . . 11
1 |
93 | 92 | eqnc 6127 |
. . . . . . . . . 10
Nc 1
Nc 1
1 1 |
94 | 89, 93 | mpbir 200 |
. . . . . . . . 9
Nc 1
Nc 1 |
95 | 85, 94 | addceq12i 4388 |
. . . . . . . 8
Nc 1 Nc 1 Nc 1 Nc 1 |
96 | 95 | oveq1i 5533 |
. . . . . . 7
Nc 1 Nc 1 ↑c 0c Nc 1
Nc 1
↑c 0c |
97 | | pw1un 4163 |
. . . . . . . . . 10
1
1
1 |
98 | 83 | ncid 6123 |
. . . . . . . . . . 11
1 Nc 1 |
99 | 92 | ncid 6123 |
. . . . . . . . . . 11
1 Nc 1 |
100 | | vn0 3557 |
. . . . . . . . . . . . . 14
|
101 | 77, 100 | xpnedisj 5513 |
. . . . . . . . . . . . 13
|
102 | | pw1eq 4143 |
. . . . . . . . . . . . 13
1
1 |
103 | 101, 102 | ax-mp 5 |
. . . . . . . . . . . 12
1
1 |
104 | | pw1in 4164 |
. . . . . . . . . . . 12
1
1
1 |
105 | | pw10 4161 |
. . . . . . . . . . . 12
1 |
106 | 103, 104,
105 | 3eqtr3i 2381 |
. . . . . . . . . . 11
1
1 |
107 | | eladdci 4399 |
. . . . . . . . . . 11
1 Nc 1 1 Nc 1 1 1
1 1
Nc 1 Nc 1 |
108 | 98, 99, 106, 107 | mp3an 1277 |
. . . . . . . . . 10
1
1
Nc 1 Nc 1 |
109 | 97, 108 | eqeltri 2423 |
. . . . . . . . 9
1
Nc 1 Nc 1 |
110 | 82, 91 | unex 4106 |
. . . . . . . . . 10
|
111 | | pw1eq 4143 |
. . . . . . . . . . 11
1 1 |
112 | 111 | eleq1d 2419 |
. . . . . . . . . 10
1 Nc 1 Nc 1 1
Nc 1 Nc 1 |
113 | 110, 112 | spcev 2946 |
. . . . . . . . 9
1
Nc 1 Nc 1 1
Nc 1 Nc 1 |
114 | 109, 113 | ax-mp 5 |
. . . . . . . 8
1 Nc 1 Nc 1 |
115 | 83 | ncelncsi 6121 |
. . . . . . . . . 10
Nc 1 NC |
116 | 92 | ncelncsi 6121 |
. . . . . . . . . 10
Nc 1
NC |
117 | | ncaddccl 6144 |
. . . . . . . . . 10
Nc 1 NC Nc 1 NC Nc 1
Nc 1 NC |
118 | 115, 116,
117 | mp2an 653 |
. . . . . . . . 9
Nc 1 Nc 1 NC |
119 | | ce0nnul 6177 |
. . . . . . . . 9
Nc 1 Nc 1
NC Nc 1 Nc 1
↑c 0c
1 Nc 1 Nc 1 |
120 | 118, 119 | ax-mp 5 |
. . . . . . . 8
Nc 1
Nc 1
↑c 0c
1 Nc 1 Nc 1 |
121 | 114, 120 | mpbir 200 |
. . . . . . 7
Nc 1 Nc 1 ↑c 0c |
122 | 96, 121 | eqnetrri 2535 |
. . . . . 6
Nc 1 Nc 1 ↑c
0c
|
123 | | addceq12 4385 |
. . . . . . . 8
Nc 1
Nc 1
Nc 1
Nc 1 |
124 | 123 | oveq1d 5537 |
. . . . . . 7
Nc 1
Nc 1
↑c 0c Nc 1
Nc 1
↑c 0c |
125 | 124 | neeq1d 2529 |
. . . . . 6
Nc 1
Nc 1
↑c 0c
Nc 1 Nc 1 ↑c
0c
|
126 | 122, 125 | mpbiri 224 |
. . . . 5
Nc 1
Nc 1
↑c 0c |
127 | 76, 126 | syl6bir 220 |
. . . 4
NC NC 1
1
↑c 0c |
128 | 127 | exlimdvv 1637 |
. . 3
NC NC 1
1
↑c 0c |
129 | 73, 128 | sylbid 206 |
. 2
NC NC
↑c 0c
↑c 0c
↑c 0c |
130 | 68, 129 | impbid 183 |
1
NC NC ↑c 0c ↑c
0c
↑c 0c |