Step |
Hyp |
Ref |
Expression |
1 |
|
poeq2 |
|
2 |
|
freq2 |
|
3 |
1 2
|
imbi12d |
|
4 |
|
poeq2 |
|
5 |
|
freq2 |
|
6 |
4 5
|
imbi12d |
|
7 |
|
poeq2 |
|
8 |
|
freq2 |
|
9 |
7 8
|
imbi12d |
|
10 |
|
poeq2 |
|
11 |
|
freq2 |
|
12 |
10 11
|
imbi12d |
|
13 |
|
fr0 |
|
14 |
13
|
a1i |
|
15 |
|
ssun1 |
|
16 |
|
poss |
|
17 |
15 16
|
ax-mp |
|
18 |
17
|
imim1i |
|
19 |
|
uncom |
|
20 |
19
|
sseq2i |
|
21 |
|
ssundif |
|
22 |
20 21
|
bitri |
|
23 |
22
|
anbi1i |
|
24 |
|
breq1 |
|
25 |
24
|
cbvrexvw |
|
26 |
|
simpllr |
|
27 |
|
simplrl |
|
28 |
|
poss |
|
29 |
28
|
impcom |
|
30 |
22 29
|
sylan2br |
|
31 |
30
|
ad2ant2r |
|
32 |
|
simpr1 |
|
33 |
|
simpr2 |
|
34 |
|
poirr |
|
35 |
34
|
3ad2antr3 |
|
36 |
|
nbrne2 |
|
37 |
33 35 36
|
syl2anc |
|
38 |
|
eldifsn |
|
39 |
32 37 38
|
sylanbrc |
|
40 |
31 39
|
sylan |
|
41 |
40
|
ne0d |
|
42 |
|
difss |
|
43 |
|
vex |
|
44 |
43
|
difexi |
|
45 |
|
fri |
|
46 |
44 45
|
mpanl1 |
|
47 |
|
ssrexv |
|
48 |
42 46 47
|
mpsyl |
|
49 |
26 27 41 48
|
syl12anc |
|
50 |
|
breq1 |
|
51 |
50
|
notbid |
|
52 |
51
|
rspcv |
|
53 |
39 52
|
syl |
|
54 |
53
|
adantr |
|
55 |
|
simplr2 |
|
56 |
|
simpll |
|
57 |
|
simplr1 |
|
58 |
|
simplr3 |
|
59 |
|
simpr |
|
60 |
|
potr |
|
61 |
56 57 58 59 60
|
syl13anc |
|
62 |
55 61
|
mpand |
|
63 |
62
|
con3d |
|
64 |
|
vex |
|
65 |
|
breq1 |
|
66 |
65
|
notbid |
|
67 |
64 66
|
ralsn |
|
68 |
63 67
|
syl6ibr |
|
69 |
54 68
|
syld |
|
70 |
|
ralun |
|
71 |
70
|
ex |
|
72 |
69 71
|
sylcom |
|
73 |
|
difsnid |
|
74 |
73
|
raleqdv |
|
75 |
58 74
|
syl |
|
76 |
72 75
|
sylibd |
|
77 |
76
|
reximdva |
|
78 |
31 77
|
sylan |
|
79 |
49 78
|
mpd |
|
80 |
79
|
3exp2 |
|
81 |
80
|
rexlimdv |
|
82 |
25 81
|
syl5bi |
|
83 |
|
ralnex |
|
84 |
|
breq2 |
|
85 |
84
|
notbid |
|
86 |
85
|
ralbidv |
|
87 |
86
|
rspcev |
|
88 |
87
|
expcom |
|
89 |
83 88
|
sylbir |
|
90 |
82 89
|
pm2.61d1 |
|
91 |
|
difsn |
|
92 |
48
|
expr |
|
93 |
|
neeq1 |
|
94 |
|
raleq |
|
95 |
94
|
rexbidv |
|
96 |
93 95
|
imbi12d |
|
97 |
92 96
|
syl5ibcom |
|
98 |
97
|
com23 |
|
99 |
98
|
adantll |
|
100 |
99
|
impr |
|
101 |
91 100
|
syl5 |
|
102 |
90 101
|
pm2.61d |
|
103 |
102
|
ex |
|
104 |
23 103
|
syl5bi |
|
105 |
104
|
alrimiv |
|
106 |
|
df-fr |
|
107 |
105 106
|
sylibr |
|
108 |
107
|
ex |
|
109 |
18 108
|
sylcom |
|
110 |
109
|
a1i |
|
111 |
3 6 9 12 14 110
|
findcard2 |
|
112 |
111
|
impcom |
|