Step |
Hyp |
Ref |
Expression |
1 |
|
pwsco2mhm.y |
|
2 |
|
pwsco2mhm.z |
|
3 |
|
pwsco2mhm.b |
|
4 |
|
pwsco2mhm.a |
|
5 |
|
pwsco2mhm.f |
|
6 |
|
mhmrcl1 |
|
7 |
5 6
|
syl |
|
8 |
1
|
pwsmnd |
|
9 |
7 4 8
|
syl2anc |
|
10 |
|
mhmrcl2 |
|
11 |
5 10
|
syl |
|
12 |
2
|
pwsmnd |
|
13 |
11 4 12
|
syl2anc |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
14 15
|
mhmf |
|
17 |
5 16
|
syl |
|
18 |
7
|
adantr |
|
19 |
4
|
adantr |
|
20 |
|
simpr |
|
21 |
1 14 3 18 19 20
|
pwselbas |
|
22 |
|
fco |
|
23 |
17 21 22
|
syl2an2r |
|
24 |
|
eqid |
|
25 |
2 15 24
|
pwselbasb |
|
26 |
11 19 25
|
syl2an2r |
|
27 |
23 26
|
mpbird |
|
28 |
27
|
fmpttd |
|
29 |
5
|
adantr |
|
30 |
29
|
adantr |
|
31 |
29 6
|
syl |
|
32 |
4
|
adantr |
|
33 |
|
simprl |
|
34 |
1 14 3 31 32 33
|
pwselbas |
|
35 |
34
|
ffvelrnda |
|
36 |
|
simprr |
|
37 |
1 14 3 31 32 36
|
pwselbas |
|
38 |
37
|
ffvelrnda |
|
39 |
|
eqid |
|
40 |
|
eqid |
|
41 |
14 39 40
|
mhmlin |
|
42 |
30 35 38 41
|
syl3anc |
|
43 |
42
|
mpteq2dva |
|
44 |
|
fvexd |
|
45 |
|
fvexd |
|
46 |
34
|
feqmptd |
|
47 |
29 16
|
syl |
|
48 |
47
|
feqmptd |
|
49 |
|
fveq2 |
|
50 |
35 46 48 49
|
fmptco |
|
51 |
37
|
feqmptd |
|
52 |
|
fveq2 |
|
53 |
38 51 48 52
|
fmptco |
|
54 |
32 44 45 50 53
|
offval2 |
|
55 |
43 54
|
eqtr4d |
|
56 |
31
|
adantr |
|
57 |
14 39
|
mndcl |
|
58 |
56 35 38 57
|
syl3anc |
|
59 |
|
eqid |
|
60 |
1 3 31 32 33 36 39 59
|
pwsplusgval |
|
61 |
|
fvexd |
|
62 |
|
fvexd |
|
63 |
32 61 62 46 51
|
offval2 |
|
64 |
60 63
|
eqtrd |
|
65 |
|
fveq2 |
|
66 |
58 64 48 65
|
fmptco |
|
67 |
29 10
|
syl |
|
68 |
|
fco |
|
69 |
47 34 68
|
syl2anc |
|
70 |
2 15 24
|
pwselbasb |
|
71 |
67 32 70
|
syl2anc |
|
72 |
69 71
|
mpbird |
|
73 |
|
fco |
|
74 |
47 37 73
|
syl2anc |
|
75 |
2 15 24
|
pwselbasb |
|
76 |
67 32 75
|
syl2anc |
|
77 |
74 76
|
mpbird |
|
78 |
|
eqid |
|
79 |
2 24 67 32 72 77 40 78
|
pwsplusgval |
|
80 |
55 66 79
|
3eqtr4d |
|
81 |
|
eqid |
|
82 |
|
coeq2 |
|
83 |
3 59
|
mndcl |
|
84 |
83
|
3expb |
|
85 |
9 84
|
sylan |
|
86 |
|
coexg |
|
87 |
5 85 86
|
syl2an2r |
|
88 |
81 82 85 87
|
fvmptd3 |
|
89 |
|
coeq2 |
|
90 |
81 89 33 72
|
fvmptd3 |
|
91 |
|
coeq2 |
|
92 |
81 91 36 77
|
fvmptd3 |
|
93 |
90 92
|
oveq12d |
|
94 |
80 88 93
|
3eqtr4d |
|
95 |
94
|
ralrimivva |
|
96 |
|
coeq2 |
|
97 |
|
eqid |
|
98 |
3 97
|
mndidcl |
|
99 |
9 98
|
syl |
|
100 |
|
coexg |
|
101 |
5 99 100
|
syl2anc |
|
102 |
81 96 99 101
|
fvmptd3 |
|
103 |
17
|
ffnd |
|
104 |
|
eqid |
|
105 |
14 104
|
mndidcl |
|
106 |
7 105
|
syl |
|
107 |
|
fcoconst |
|
108 |
103 106 107
|
syl2anc |
|
109 |
1 104
|
pws0g |
|
110 |
7 4 109
|
syl2anc |
|
111 |
110
|
coeq2d |
|
112 |
|
eqid |
|
113 |
104 112
|
mhm0 |
|
114 |
5 113
|
syl |
|
115 |
114
|
sneqd |
|
116 |
115
|
xpeq2d |
|
117 |
108 111 116
|
3eqtr3d |
|
118 |
2 112
|
pws0g |
|
119 |
11 4 118
|
syl2anc |
|
120 |
102 117 119
|
3eqtrd |
|
121 |
28 95 120
|
3jca |
|
122 |
|
eqid |
|
123 |
3 24 59 78 97 122
|
ismhm |
|
124 |
9 13 121 123
|
syl21anbrc |
|