Description: No member of a cardinal number of a set is equinumerous to the set. Proposition 10.6(2) of TakeutiZaring p. 85. (Contributed by Mario Carneiro, 9-Jan-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | cardne | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfvdm | |
|
2 | cardon | |
|
3 | 2 | oneli | |
4 | breq1 | |
|
5 | 4 | onintss | |
6 | 3 5 | syl | |
7 | 6 | adantl | |
8 | cardval3 | |
|
9 | 8 | sseq1d | |
10 | 9 | adantr | |
11 | 7 10 | sylibrd | |
12 | ontri1 | |
|
13 | 2 3 12 | sylancr | |
14 | 13 | adantl | |
15 | 11 14 | sylibd | |
16 | 15 | con2d | |
17 | 16 | ex | |
18 | 17 | pm2.43d | |
19 | 1 18 | mpcom | |