Step |
Hyp |
Ref |
Expression |
1 |
|
fucpropd.1 |
|
2 |
|
fucpropd.2 |
|
3 |
|
fucpropd.3 |
|
4 |
|
fucpropd.4 |
|
5 |
|
fucpropd.a |
|
6 |
|
fucpropd.b |
|
7 |
|
fucpropd.c |
|
8 |
|
fucpropd.d |
|
9 |
1 2 3 4 5 6 7 8
|
funcpropd |
|
10 |
9
|
adantr |
|
11 |
|
nfv |
|
12 |
|
nfcsb1v |
|
13 |
12
|
a1i |
|
14 |
|
fvexd |
|
15 |
|
nfv |
|
16 |
|
nfcsb1v |
|
17 |
16
|
a1i |
|
18 |
|
fvexd |
|
19 |
|
eqid |
|
20 |
|
eqid |
|
21 |
|
eqid |
|
22 |
3
|
ad4antr |
|
23 |
|
eqid |
|
24 |
|
simplr |
|
25 |
|
relfunc |
|
26 |
|
simpllr |
|
27 |
26
|
simpld |
|
28 |
|
1st2ndbr |
|
29 |
25 27 28
|
sylancr |
|
30 |
24 29
|
eqbrtrd |
|
31 |
23 19 30
|
funcf1 |
|
32 |
31
|
ffvelrnda |
|
33 |
|
simpr |
|
34 |
26
|
simprd |
|
35 |
|
1st2ndbr |
|
36 |
25 34 35
|
sylancr |
|
37 |
33 36
|
eqbrtrd |
|
38 |
23 19 37
|
funcf1 |
|
39 |
38
|
ffvelrnda |
|
40 |
19 20 21 22 32 39
|
homfeqval |
|
41 |
40
|
ixpeq2dva |
|
42 |
1
|
homfeqbas |
|
43 |
42
|
ad3antrrr |
|
44 |
43
|
ixpeq1d |
|
45 |
41 44
|
eqtrd |
|
46 |
|
fveq2 |
|
47 |
|
fveq2 |
|
48 |
46 47
|
oveq12d |
|
49 |
48
|
cbvixpv |
|
50 |
49
|
eleq2i |
|
51 |
43
|
adantr |
|
52 |
51
|
adantr |
|
53 |
|
eqid |
|
54 |
|
eqid |
|
55 |
1
|
ad6antr |
|
56 |
|
simplr |
|
57 |
|
simpr |
|
58 |
23 53 54 55 56 57
|
homfeqval |
|
59 |
|
eqid |
|
60 |
|
eqid |
|
61 |
3
|
ad7antr |
|
62 |
4
|
ad7antr |
|
63 |
32
|
ad5ant13 |
|
64 |
31
|
ad2antrr |
|
65 |
64
|
ffvelrnda |
|
66 |
65
|
adantr |
|
67 |
38
|
ad2antrr |
|
68 |
67
|
ffvelrnda |
|
69 |
68
|
adantr |
|
70 |
30
|
ad3antrrr |
|
71 |
23 53 20 70 56 57
|
funcf2 |
|
72 |
71
|
ffvelrnda |
|
73 |
|
fveq2 |
|
74 |
|
fveq2 |
|
75 |
73 74
|
oveq12d |
|
76 |
75
|
fvixp |
|
77 |
76
|
ad5ant24 |
|
78 |
19 20 59 60 61 62 63 66 69 72 77
|
comfeqval |
|
79 |
39
|
ad5ant13 |
|
80 |
|
fveq2 |
|
81 |
|
fveq2 |
|
82 |
80 81
|
oveq12d |
|
83 |
82
|
fvixp |
|
84 |
83
|
ad5ant23 |
|
85 |
37
|
ad3antrrr |
|
86 |
23 53 20 85 56 57
|
funcf2 |
|
87 |
86
|
ffvelrnda |
|
88 |
19 20 59 60 61 62 63 79 69 84 87
|
comfeqval |
|
89 |
78 88
|
eqeq12d |
|
90 |
58 89
|
raleqbidva |
|
91 |
52 90
|
raleqbidva |
|
92 |
51 91
|
raleqbidva |
|
93 |
50 92
|
sylan2b |
|
94 |
45 93
|
rabeqbidva |
|
95 |
|
csbeq1a |
|
96 |
95
|
adantl |
|
97 |
94 96
|
eqtrd |
|
98 |
15 17 18 97
|
csbiedf |
|
99 |
|
csbeq1a |
|
100 |
99
|
adantl |
|
101 |
98 100
|
eqtrd |
|
102 |
11 13 14 101
|
csbiedf |
|
103 |
9 10 102
|
mpoeq123dva |
|
104 |
|
eqid |
|
105 |
104 23 53 20 59
|
natfval |
|
106 |
|
eqid |
|
107 |
|
eqid |
|
108 |
106 107 54 21 60
|
natfval |
|
109 |
103 105 108
|
3eqtr4g |
|