al.dfbi

Theorem.

Arguments:

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

Assertions:

(forallx(phileftrightarrowpsi)leftrightarrow(forallx(phitopsi)wedgeforallx(psitophi)))

Proof:

Hyp Ref Line Expr
dfbi1((phileftrightarrowpsi)leftrightarrow((phitopsi)wedge(psitophi)))
1eqt-∀-i2(forallx(phileftrightarrowpsi)leftrightarrowforallx((phitopsi)wedge(psitophi)))
al.andi3(forallx((phitopsi)wedge(psitophi))leftrightarrow(forallx(phitopsi)wedgeforallx(psitophi)))
2, 3bitr4(forallx(phileftrightarrowpsi)leftrightarrow(forallx(phitopsi)wedgeforallx(psitophi)))