alrot4

Theorem.

Arguments:

x (sv), y (sv), z (sv), w (sv), phi (pr),

Assertions:

(forallxforallyforallzforallwphileftrightarrowforallzforallwforallxforallyphi)

Proof:

Hyp Ref Line Expr
alcom1(forallyforallzforallwphileftrightarrowforallzforallyforallwphi)
alcom2(forallyforallwphileftrightarrowforallwforallyphi)
2eqt-∀-i3(forallzforallyforallwphileftrightarrowforallzforallwforallyphi)
1, 3bitr4(forallyforallzforallwphileftrightarrowforallzforallwforallyphi)
4eqt-∀-i5(forallxforallyforallzforallwphileftrightarrowforallxforallzforallwforallyphi)
alcom6(forallxforallzforallwforallyphileftrightarrowforallzforallxforallwforallyphi)
alcom7(forallxforallwforallyphileftrightarrowforallwforallxforallyphi)
7eqt-∀-i8(forallzforallxforallwforallyphileftrightarrowforallzforallwforallxforallyphi)
5, 6, 82bitr9(forallxforallyforallzforallwphileftrightarrowforallzforallwforallxforallyphi)