Description: A variable not free in a proposition remains so after substitution in that proposition with a distinct variable. Usage of this theorem is discouraged because it depends on ax-13 . Theorem nfsb replaces the distinctor with a disjoint variable condition. Visit also nfsbv for a weaker version of nfsb not requiring ax-13 . (Contributed by NM, 14-May-1993) (Revised by Mario Carneiro, 4-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nfsb4.1 | |- F/ z ph |
|
| Assertion | nfsb4 | |- ( -. A. z z = y -> F/ z [ y / x ] ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfsb4.1 | |- F/ z ph |
|
| 2 | nfsb4t | |- ( A. x F/ z ph -> ( -. A. z z = y -> F/ z [ y / x ] ph ) ) |
|
| 3 | 2 1 | mpg | |- ( -. A. z z = y -> F/ z [ y / x ] ph ) |