Description: Strong (or "total") induction principle over the naturals. (Contributed by Scott Fenton, 16-May-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | nnsinds.1 | ||
nnsinds.2 | |||
nnsinds.3 | |||
Assertion | nnsinds |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnsinds.1 | ||
2 | nnsinds.2 | ||
3 | nnsinds.3 | ||
4 | elnnuz | ||
5 | elnnuz | ||
6 | 5 3 | sylbir | |
7 | 1 2 6 | uzsinds | |
8 | 4 7 | sylbi |