sb-negw

Theorem.

Arguments:

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

Distinct variable conditions:

(a, x),

Assertions:

([a/x]lnotphileftrightarrowlnot[a/x]phi)

Proof:

Hyp Ref Line Expr
dfsb-dvex1([a/x]phileftrightarrowexistsx((xeqa)wedgephi))
1bi.bldneg2(lnot[a/x]phileftrightarrowlnotexistsx((xeqa)wedgephi))
aln.ex3(forallxlnot((xeqa)wedgephi)leftrightarrowlnotexistsx((xeqa)wedgephi))
2, 3><bitr4(forallxlnot((xeqa)wedgephi)leftrightarrowlnot[a/x]phi)
im.nan5(((xeqa)tolnotphi)leftrightarrowlnot((xeqa)wedgephi))
5eqt-∀-i6(forallx((xeqa)tolnotphi)leftrightarrowforallxlnot((xeqa)wedgephi))
dfsb-dval7([a/x]lnotphileftrightarrowforallx((xeqa)tolnotphi))
4, 6, 72bitr8([a/x]lnotphileftrightarrowlnot[a/x]phi)