drex1

Theorem.

Arguments:

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

Hypotheses:

(forallx(xeqy)to(phileftrightarrowpsi))

Assertions:

(forallx(xeqy)to(existsxphileftrightarrowexistsypsi))

Proof:

Hyp Ref Line Expr
Hypo1(forallx(xeqy)to(phileftrightarrowpsi))
1bi.bldnegd2(forallx(xeqy)to(lnotphileftrightarrowlnotpsi))
2dral13(forallx(xeqy)to(forallxlnotphileftrightarrowforallylnotpsi))
3bi.bldnegd4(forallx(xeqy)to(lnotforallxlnotphileftrightarrowlnotforallylnotpsi))
df-ex5(existsxphileftrightarrowlnotforallxlnotphi)
df-ex6(existsypsileftrightarrowlnotforallylnotpsi)
4, 5, 6<2bitrg7(forallx(xeqy)to(existsxphileftrightarrowexistsypsi))