Step | Hyp | Ref
| Expression |
1 | | fnpw1fn 5853 |
. 2
Pw1Fn 1c |
2 | | df-pw1fn 5766 |
. . . 4
Pw1Fn 1c 1 |
3 | 2 | rnmpt 5686 |
. . 3
Pw1Fn
1c
1 |
4 | | vex 2862 |
. . . . . . 7
|
5 | 4 | sspw1 4335 |
. . . . . 6
1
1 |
6 | | df1c2 4168 |
. . . . . . 7
1c
1 |
7 | 6 | sseq2i 3296 |
. . . . . 6
1c 1 |
8 | | ssv 3291 |
. . . . . . . 8
|
9 | 8 | biantrur 492 |
. . . . . . 7
1
1 |
10 | 9 | exbii 1582 |
. . . . . 6
1 1 |
11 | 5, 7, 10 | 3bitr4i 268 |
. . . . 5
1c 1 |
12 | 4 | elpw 3728 |
. . . . 5
1c
1c |
13 | | df-rex 2620 |
. . . . . 6
1c
1 1c
1 |
14 | | el1c 4139 |
. . . . . . . . 9
1c
|
15 | 14 | anbi1i 676 |
. . . . . . . 8
1c 1
1 |
16 | | 19.41v 1901 |
. . . . . . . 8
1
1 |
17 | 15, 16 | bitr4i 243 |
. . . . . . 7
1c 1
1 |
18 | 17 | exbii 1582 |
. . . . . 6
1c 1 1 |
19 | | excom 1741 |
. . . . . . 7
1
1 |
20 | | snex 4111 |
. . . . . . . . 9
|
21 | | unieq 3900 |
. . . . . . . . . . . 12
|
22 | | vex 2862 |
. . . . . . . . . . . . 13
|
23 | 22 | unisn 3907 |
. . . . . . . . . . . 12
|
24 | 21, 23 | syl6eq 2401 |
. . . . . . . . . . 11
|
25 | | pw1eq 4143 |
. . . . . . . . . . 11
1 1 |
26 | 24, 25 | syl 15 |
. . . . . . . . . 10
1 1 |
27 | 26 | eqeq2d 2364 |
. . . . . . . . 9
1 1 |
28 | 20, 27 | ceqsexv 2894 |
. . . . . . . 8
1 1 |
29 | 28 | exbii 1582 |
. . . . . . 7
1
1 |
30 | 19, 29 | bitri 240 |
. . . . . 6
1
1 |
31 | 13, 18, 30 | 3bitri 262 |
. . . . 5
1c
1 1 |
32 | 11, 12, 31 | 3bitr4i 268 |
. . . 4
1c 1c 1 |
33 | 32 | abbi2i 2464 |
. . 3
1c
1c
1 |
34 | 3, 33 | eqtr4i 2376 |
. 2
Pw1Fn 1c |
35 | | el1c 4139 |
. . . . . 6
1c
|
36 | | el1c 4139 |
. . . . . 6
1c
|
37 | 35, 36 | anbi12i 678 |
. . . . 5
1c 1c
|
38 | | eeanv 1913 |
. . . . 5
|
39 | 37, 38 | bitr4i 243 |
. . . 4
1c 1c |
40 | | pw111 4170 |
. . . . . . . 8
1
1 |
41 | 40 | biimpi 186 |
. . . . . . 7
1
1
|
42 | 41 | a1i 10 |
. . . . . 6
1 1
|
43 | | fveq2 5328 |
. . . . . . . 8
Pw1Fn Pw1Fn |
44 | | vex 2862 |
. . . . . . . . 9
|
45 | 44 | pw1fnval 5851 |
. . . . . . . 8
Pw1Fn
1 |
46 | 43, 45 | syl6eq 2401 |
. . . . . . 7
Pw1Fn 1 |
47 | | fveq2 5328 |
. . . . . . . 8
Pw1Fn Pw1Fn |
48 | | vex 2862 |
. . . . . . . . 9
|
49 | 48 | pw1fnval 5851 |
. . . . . . . 8
Pw1Fn
1 |
50 | 47, 49 | syl6eq 2401 |
. . . . . . 7
Pw1Fn 1 |
51 | 46, 50 | eqeqan12d 2368 |
. . . . . 6
Pw1Fn
Pw1Fn 1
1 |
52 | | eqeq12 2365 |
. . . . . . 7
|
53 | 44 | sneqb 3876 |
. . . . . . 7
|
54 | 52, 53 | syl6bb 252 |
. . . . . 6
|
55 | 42, 51, 54 | 3imtr4d 259 |
. . . . 5
Pw1Fn
Pw1Fn |
56 | 55 | exlimivv 1635 |
. . . 4
Pw1Fn
Pw1Fn |
57 | 39, 56 | sylbi 187 |
. . 3
1c 1c
Pw1Fn Pw1Fn |
58 | 57 | rgen2a 2680 |
. 2
1c
1c Pw1Fn Pw1Fn |
59 | | dff1o6 5475 |
. 2
Pw1Fn 1c1c Pw1Fn 1c
Pw1Fn 1c 1c 1c
Pw1Fn Pw1Fn |
60 | 1, 34, 58, 59 | mpbir3an 1134 |
1
Pw1Fn 1c1c |