Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 14-May-1993)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbh.1 | |- ( ph -> A. x ph ) |
|
| Assertion | sbh | |- ( [ y / x ] ph <-> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbh.1 | |- ( ph -> A. x ph ) |
|
| 2 | 1 | nf5i | |- F/ x ph |
| 3 | 2 | sbf | |- ( [ y / x ] ph <-> ph ) |