Description: Rule used to change the bound variable in a universal quantifier with implicit substitution. Deduction form. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvaldvaw if possible. (Contributed by David Moews, 1-May-2017) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | cbvaldva.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
Assertion | cbvaldva | |- ( ph -> ( A. x ps <-> A. y ch ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvaldva.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
2 | nfv | |- F/ y ph |
|
3 | nfvd | |- ( ph -> F/ y ps ) |
|
4 | 1 | ex | |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) |
5 | 2 3 4 | cbvald | |- ( ph -> ( A. x ps <-> A. y ch ) ) |