cbv-∃mo

Theorem.

Arguments:

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

Distinct variable conditions:

(x, y),

Hypotheses:

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

Assertions:

(_em1xphileftrightarrow_em1ypsi)

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phileftrightarrowpsi))
2(x bound in psi)
3(y bound in phi)
1, 2, 3cbvex4(existsxphileftrightarrowexistsypsi)
1, 2, 3cbv-∃15(_e1xphileftrightarrow_e1ypsi)
4, 5bi.bldim<>6((existsxphito_e1xphi)leftrightarrow(existsypsito_e1ypsi))
df-∃mo7(_em1xphileftrightarrow(existsxphito_e1xphi))
df-∃mo8(_em1ypsileftrightarrow(existsypsito_e1ypsi))
6, 7, 8<2bitr9(_em1xphileftrightarrow_em1ypsi)