Step |
Hyp |
Ref |
Expression |
1 |
|
salexct.a |
|
2 |
|
salexct.b |
|
3 |
1
|
pwexd |
|
4 |
|
rabexg |
|
5 |
3 4
|
syl |
|
6 |
2 5
|
eqeltrid |
|
7 |
|
0elpw |
|
8 |
7
|
a1i |
|
9 |
|
0fin |
|
10 |
|
fict |
|
11 |
9 10
|
ax-mp |
|
12 |
11
|
orci |
|
13 |
12
|
a1i |
|
14 |
8 13
|
jca |
|
15 |
|
breq1 |
|
16 |
|
difeq2 |
|
17 |
16
|
breq1d |
|
18 |
15 17
|
orbi12d |
|
19 |
18 2
|
elrab2 |
|
20 |
14 19
|
sylibr |
|
21 |
|
snidg |
|
22 |
|
snelpwi |
|
23 |
|
snfi |
|
24 |
|
fict |
|
25 |
23 24
|
ax-mp |
|
26 |
25
|
orci |
|
27 |
26
|
a1i |
|
28 |
22 27
|
jca |
|
29 |
|
breq1 |
|
30 |
|
difeq2 |
|
31 |
30
|
breq1d |
|
32 |
29 31
|
orbi12d |
|
33 |
32 2
|
elrab2 |
|
34 |
28 33
|
sylibr |
|
35 |
|
elunii |
|
36 |
21 34 35
|
syl2anc |
|
37 |
36
|
rgen |
|
38 |
|
dfss3 |
|
39 |
37 38
|
mpbir |
|
40 |
|
ssrab2 |
|
41 |
2 40
|
eqsstri |
|
42 |
41
|
unissi |
|
43 |
|
unipw |
|
44 |
42 43
|
sseqtri |
|
45 |
39 44
|
eqssi |
|
46 |
|
difssd |
|
47 |
1 46
|
ssexd |
|
48 |
|
elpwg |
|
49 |
47 48
|
syl |
|
50 |
46 49
|
mpbird |
|
51 |
50
|
ad2antrr |
|
52 |
41
|
sseli |
|
53 |
|
elpwi |
|
54 |
52 53
|
syl |
|
55 |
|
dfss4 |
|
56 |
54 55
|
sylib |
|
57 |
56
|
ad2antlr |
|
58 |
|
simpr |
|
59 |
57 58
|
eqbrtrd |
|
60 |
|
olc |
|
61 |
59 60
|
syl |
|
62 |
51 61
|
jca |
|
63 |
|
breq1 |
|
64 |
|
difeq2 |
|
65 |
64
|
breq1d |
|
66 |
63 65
|
orbi12d |
|
67 |
|
breq1 |
|
68 |
|
difeq2 |
|
69 |
68
|
breq1d |
|
70 |
67 69
|
orbi12d |
|
71 |
70
|
cbvrabv |
|
72 |
2 71
|
eqtri |
|
73 |
66 72
|
elrab2 |
|
74 |
62 73
|
sylibr |
|
75 |
50
|
ad2antrr |
|
76 |
2
|
rabeq2i |
|
77 |
76
|
biimpi |
|
78 |
77
|
simprd |
|
79 |
78
|
adantl |
|
80 |
79
|
adantr |
|
81 |
|
simpr |
|
82 |
|
pm2.53 |
|
83 |
80 81 82
|
sylc |
|
84 |
|
orc |
|
85 |
83 84
|
syl |
|
86 |
75 85
|
jca |
|
87 |
86 73
|
sylibr |
|
88 |
74 87
|
pm2.61dan |
|
89 |
|
elpwi |
|
90 |
89
|
adantr |
|
91 |
|
simpr |
|
92 |
90 91
|
sseldd |
|
93 |
41
|
sseli |
|
94 |
|
elpwi |
|
95 |
93 94
|
syl |
|
96 |
92 95
|
syl |
|
97 |
96
|
ralrimiva |
|
98 |
|
unissb |
|
99 |
97 98
|
sylibr |
|
100 |
|
vuniex |
|
101 |
100
|
elpw |
|
102 |
99 101
|
sylibr |
|
103 |
102
|
adantr |
|
104 |
|
id |
|
105 |
104
|
adantll |
|
106 |
|
unictb |
|
107 |
|
orc |
|
108 |
105 106 107
|
3syl |
|
109 |
|
rexnal |
|
110 |
109
|
bicomi |
|
111 |
110
|
biimpi |
|
112 |
111
|
adantl |
|
113 |
|
nfv |
|
114 |
|
nfra1 |
|
115 |
114
|
nfn |
|
116 |
113 115
|
nfan |
|
117 |
|
nfv |
|
118 |
|
elssuni |
|
119 |
118
|
3ad2ant2 |
|
120 |
119
|
sscond |
|
121 |
92
|
3adant3 |
|
122 |
|
simp3 |
|
123 |
72
|
rabeq2i |
|
124 |
123
|
biimpi |
|
125 |
124
|
simprd |
|
126 |
125
|
adantr |
|
127 |
|
simpr |
|
128 |
|
pm2.53 |
|
129 |
126 127 128
|
sylc |
|
130 |
121 122 129
|
syl2anc |
|
131 |
|
ssct |
|
132 |
120 130 131
|
syl2anc |
|
133 |
132
|
3exp |
|
134 |
133
|
adantr |
|
135 |
116 117 134
|
rexlimd |
|
136 |
112 135
|
mpd |
|
137 |
|
olc |
|
138 |
136 137
|
syl |
|
139 |
138
|
adantlr |
|
140 |
108 139
|
pm2.61dan |
|
141 |
103 140
|
jca |
|
142 |
|
breq1 |
|
143 |
|
difeq2 |
|
144 |
143
|
breq1d |
|
145 |
142 144
|
orbi12d |
|
146 |
145 72
|
elrab2 |
|
147 |
141 146
|
sylibr |
|
148 |
147
|
3adant1 |
|
149 |
6 20 45 88 148
|
issald |
|