2al.dfbi

Theorem.

Arguments:

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

Assertions:

(forallxforally(phileftrightarrowpsi)leftrightarrow(forallxforally(phitopsi)wedgeforallxforally(psitophi)))

Proof:

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