Description: A strictly monotone ordinal function preserves the membership relation. (Contributed by Mario Carneiro, 12-Mar-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | smoel2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fndm | |
|
2 | 1 | eleq2d | |
3 | 2 | anbi1d | |
4 | 3 | biimprd | |
5 | smoel | |
|
6 | 5 | 3expib | |
7 | 4 6 | sylan9 | |
8 | 7 | imp | |