dfsb-dval

Theorem.

Arguments:

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

Distinct variable conditions:

(y, x),

Assertions:

([y/x]phileftrightarrowforallx((xeqy)tophi))

Proof:

Hyp Ref Line Expr
dfsb-dvex1([y/x]phileftrightarrowexistsx((xeqy)wedgephi))
eqs4lem2(forallx((xeqy)tophi)toexistsx((xeqy)wedgephi))
eqs5lem3(existsx((xeqy)wedgephi)toforallx((xeqy)tophi))
2, 3>bii4(existsx((xeqy)wedgephi)leftrightarrowforallx((xeqy)tophi))
1, 4bitr5([y/x]phileftrightarrowforallx((xeqy)tophi))