Metamath Proof Explorer


Theorem 3exbidv

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 ) )

Proof

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 ) )