Description: Bound-variable hypothesis builder for class substitution. Version of nfsbc with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 7-Sep-2014) (Revised by Gino Giotto, 10-Jan-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfsbcw.1 | |- F/_ x A |
|
| nfsbcw.2 | |- F/ x ph |
||
| Assertion | nfsbcw | |- F/ x [. A / y ]. ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfsbcw.1 | |- F/_ x A |
|
| 2 | nfsbcw.2 | |- F/ x ph |
|
| 3 | nftru | |- F/ y T. |
|
| 4 | 1 | a1i | |- ( T. -> F/_ x A ) |
| 5 | 2 | a1i | |- ( T. -> F/ x ph ) |
| 6 | 3 4 5 | nfsbcdw | |- ( T. -> F/ x [. A / y ]. ph ) |
| 7 | 6 | mptru | |- F/ x [. A / y ]. ph |