Description: If y is not free in ph , x is not free in [ y / x ] ph . Usage of this theorem is discouraged because it depends on ax-13 . Check out nfs1v for a version requiring fewer axioms. (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nfs1.1 | |- F/ y ph |
|
| Assertion | nfs1 | |- F/ x [ y / x ] ph |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfs1.1 | |- F/ y ph |
|
| 2 | 1 | nf5ri | |- ( ph -> A. y ph ) |
| 3 | 2 | hbsb3 | |- ( [ y / x ] ph -> A. x [ y / x ] ph ) |
| 4 | 3 | nf5i | |- F/ x [ y / x ] ph |