bv-↔

Theorem.

Arguments:

phi (pr), psi (pr), x (sv),

Hypotheses:

(x bound in psi)
(x bound in phi)

Assertions:

(x bound in (phileftrightarrowpsi))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in psi)
2(x bound in phi)
1, 2bv-→3(x bound in (phitopsi))
1, 2bv-→4(x bound in (psitophi))
3, 4bv-∧5(x bound in ((phitopsi)wedge(psitophi)))
dfbi6((phileftrightarrowpsi)leftrightarrow((phitopsi)wedge(psitophi)))
5, 6bvdef7(x bound in (phileftrightarrowpsi))