ax4c

Theorem.

Arguments:

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

Hypotheses:

((xeqy)to(phitopsi))
(x bound in phi)

Assertions:

(phitoexistsxpsi)

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phitopsi))
2(x bound in phi)
2bv-¬3(x bound in lnotphi)
1con4((xeqy)to(lnotpsitolnotphi))
3, 4ax4a5(forallxlnotpsitolnotphi)
5con>6(phitolnotforallxlnotpsi)
df-ex7(existsxpsileftrightarrowlnotforallxlnotpsi)
6, 7brpi22<8(phitoexistsxpsi)