Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 11-Oct-2004) (Proof shortened by Andrew Salmon, 29-Jun-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sbcgf.1 | |- F/ x ph |
|
| Assertion | sbcgf | |- ( A e. V -> ( [. A / x ]. ph <-> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbcgf.1 | |- F/ x ph |
|
| 2 | sbctt | |- ( ( A e. V /\ F/ x ph ) -> ( [. A / x ]. ph <-> ph ) ) |
|
| 3 | 1 2 | mpan2 | |- ( A e. V -> ( [. A / x ]. ph <-> ph ) ) |