Description: Formula-building rule for three existential quantifiers (deduction form). (Contributed by NM, 1-May-1995)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 3exbidv.1 | |- ( ph -> ( ps <-> ch ) ) |
|
Assertion | 3exbidv | |- ( ph -> ( E. x E. y E. z ps <-> E. x E. y E. z ch ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3exbidv.1 | |- ( ph -> ( ps <-> ch ) ) |
|
2 | 1 | exbidv | |- ( ph -> ( E. z ps <-> E. z ch ) ) |
3 | 2 | 2exbidv | |- ( ph -> ( E. x E. y E. z ps <-> E. x E. y E. z ch ) ) |