Description: Bound-variable hypothesis builder for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018) (Proof shortened by AV, 10-Oct-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | nfwsuc.1 | |- F/_ x R |
|
nfwsuc.2 | |- F/_ x A |
||
nfwsuc.3 | |- F/_ x X |
||
Assertion | nfwsuc | |- F/_ x wsuc ( R , A , X ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfwsuc.1 | |- F/_ x R |
|
2 | nfwsuc.2 | |- F/_ x A |
|
3 | nfwsuc.3 | |- F/_ x X |
|
4 | df-wsuc | |- wsuc ( R , A , X ) = inf ( Pred ( `' R , A , X ) , A , R ) |
|
5 | 1 | nfcnv | |- F/_ x `' R |
6 | 5 2 3 | nfpred | |- F/_ x Pred ( `' R , A , X ) |
7 | 6 2 1 | nfinf | |- F/_ x inf ( Pred ( `' R , A , X ) , A , R ) |
8 | 4 7 | nfcxfr | |- F/_ x wsuc ( R , A , X ) |