Step |
Hyp |
Ref |
Expression |
1 |
|
noextend.1 |
|
2 |
|
nofun |
|
3 |
|
fnconstg |
|
4 |
|
fnfun |
|
5 |
1 3 4
|
mp2b |
|
6 |
|
snnzg |
|
7 |
|
dmxp |
|
8 |
1 6 7
|
mp2b |
|
9 |
8
|
ineq2i |
|
10 |
|
disjdif |
|
11 |
9 10
|
eqtri |
|
12 |
|
funun |
|
13 |
11 12
|
mpan2 |
|
14 |
2 5 13
|
sylancl |
|
15 |
14
|
adantr |
|
16 |
|
dmun |
|
17 |
8
|
uneq2i |
|
18 |
16 17
|
eqtri |
|
19 |
|
nodmon |
|
20 |
|
undif |
|
21 |
|
eleq1a |
|
22 |
21
|
adantl |
|
23 |
20 22
|
syl5bi |
|
24 |
|
ssdif0 |
|
25 |
|
uneq2 |
|
26 |
|
un0 |
|
27 |
25 26
|
eqtrdi |
|
28 |
27
|
eleq1d |
|
29 |
28
|
biimprcd |
|
30 |
29
|
adantr |
|
31 |
24 30
|
syl5bi |
|
32 |
|
eloni |
|
33 |
|
eloni |
|
34 |
|
ordtri2or2 |
|
35 |
32 33 34
|
syl2an |
|
36 |
23 31 35
|
mpjaod |
|
37 |
19 36
|
sylan |
|
38 |
18 37
|
eqeltrid |
|
39 |
|
rnun |
|
40 |
|
norn |
|
41 |
40
|
adantr |
|
42 |
|
rnxpss |
|
43 |
|
snssi |
|
44 |
1 43
|
ax-mp |
|
45 |
42 44
|
sstri |
|
46 |
|
unss |
|
47 |
41 45 46
|
sylanblc |
|
48 |
39 47
|
eqsstrid |
|
49 |
|
elno2 |
|
50 |
15 38 48 49
|
syl3anbrc |
|