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Metamath Proof Explorer
Description: Existential specialization, using implicit substitution, deduction
version. (Contributed by RP, 12-Aug-2020) (Revised by AV, 16-Aug-2024)
|
|
Ref |
Expression |
|
Hypotheses |
spcedv.1 |
|- ( ph -> X e. V ) |
|
|
spcedv.2 |
|- ( ph -> ch ) |
|
|
spcedv.3 |
|- ( x = X -> ( ps <-> ch ) ) |
|
Assertion |
spcedv |
|- ( ph -> E. x ps ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
spcedv.1 |
|- ( ph -> X e. V ) |
| 2 |
|
spcedv.2 |
|- ( ph -> ch ) |
| 3 |
|
spcedv.3 |
|- ( x = X -> ( ps <-> ch ) ) |
| 4 |
3
|
spcegv |
|- ( X e. V -> ( ch -> E. x ps ) ) |
| 5 |
1 2 4
|
sylc |
|- ( ph -> E. x ps ) |