eqt-∃mo-d

Theorem.

Arguments:

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

Hypotheses:

(phito(psileftrightarrowchi))
(x bound in phi)

Assertions:

(phito(_em1xpsileftrightarrow_em1xchi))

Proof:

Hyp Ref Line Expr
Hypo1(phito(psileftrightarrowchi))
2(x bound in phi)
1, 2bi.bldexd3(phito(existsxpsileftrightarrowexistsxchi))
1, 2eqt-∃1-d4(phito(_e1xpsileftrightarrow_e1xchi))
3, 4bi.bldim<>d5(phito((existsxpsito_e1xpsi)leftrightarrow(existsxchito_e1xchi)))
df-∃mo6(_em1xpsileftrightarrow(existsxpsito_e1xpsi))
df-∃mo7(_em1xchileftrightarrow(existsxchito_e1xchi))
5, 6, 7<2bitrg8(phito(_em1xpsileftrightarrow_em1xchi))