Description: If z is not free in ph , it is not free in [ y / x ] ph when y and z are distinct. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker hbsbw when possible. (Contributed by NM, 12-Aug-1993) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | hbsb.1 | |- ( ph -> A. z ph ) |
|
| Assertion | hbsb | |- ( [ y / x ] ph -> A. z [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hbsb.1 | |- ( ph -> A. z ph ) |
|
| 2 | 1 | nf5i | |- F/ z ph |
| 3 | 2 | nfsb | |- F/ z [ y / x ] ph |
| 4 | 3 | nf5ri | |- ( [ y / x ] ph -> A. z [ y / x ] ph ) |