Theorem sb8e

Substitution of variable in existential quantifier. Usage of this theorem is discouraged because it depends on [ax-13]. For a version requiring disjoint variables, but fewer axioms, see sb8ef. (Contributed by NM, 12-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Jim Kingdon, 15-Jan-2018.) (New usage is discouraged.)

Hypothesis
sb8.1
\( \vdash \Finv y \, \varphi \)
Conclusion
\( \vdash \exists x \, \varphi \leftrightarrow \exists y \, [ y / x ] \, \varphi \)
Proof
l0
sb8.1
sb8.1
l2
nfs1 _
sbequ12
cbvex l0 l2 _