Description: The other element of a pair is an element of the pair. (Contributed by Thierry Arnoux, 26-Aug-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | unidifsnel | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2onn | |
|
2 | nnfi | |
|
3 | 1 2 | ax-mp | |
4 | enfi | |
|
5 | 3 4 | mpbiri | |
6 | 5 | adantl | |
7 | diffi | |
|
8 | 6 7 | syl | |
9 | 8 | cardidd | |
10 | 9 | ensymd | |
11 | simpl | |
|
12 | dif1card | |
|
13 | 6 11 12 | syl2anc | |
14 | cardennn | |
|
15 | 1 14 | mpan2 | |
16 | df-2o | |
|
17 | 15 16 | eqtrdi | |
18 | 17 | adantl | |
19 | 13 18 | eqtr3d | |
20 | suc11reg | |
|
21 | 19 20 | sylib | |
22 | 10 21 | breqtrd | |
23 | en1 | |
|
24 | 22 23 | sylib | |
25 | simpr | |
|
26 | 25 | unieqd | |
27 | unisnv | |
|
28 | 26 27 | eqtrdi | |
29 | difssd | |
|
30 | 25 29 | eqsstrrd | |
31 | vsnid | |
|
32 | ssel2 | |
|
33 | 30 31 32 | sylancl | |
34 | 28 33 | eqeltrd | |
35 | 24 34 | exlimddv | |