eqsex

Theorem.

Arguments:

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

Distinct variable conditions:

(x, y),

Hypotheses:

((xeqy)to(phileftrightarrowpsi))
(x bound in psi)

Assertions:

(existsx((xeqy)wedgephi)leftrightarrowpsi)

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phileftrightarrowpsi))
2(x bound in psi)
exn.al3(existsxlnot((xeqy)tolnotphi)leftrightarrowlnotforallx((xeqy)tolnotphi))
df-an4(((xeqy)wedgephi)leftrightarrowlnot((xeqy)tolnotphi))
4eqt-∃-i5(existsx((xeqy)wedgephi)leftrightarrowexistsxlnot((xeqy)tolnotphi))
2bv-¬6(x bound in lnotpsi)
1bi.bldnegd7((xeqy)to(lnotphileftrightarrowlnotpsi))
6, 7eqsal8(forallx((xeqy)tolnotphi)leftrightarrowlnotpsi)
8conb>i9(psileftrightarrowlnotforallx((xeqy)tolnotphi))
3, 5, 9<2bitr10(existsx((xeqy)wedgephi)leftrightarrowpsi)