Theorem sb5rf

Reversed substitution. Usage of this theorem is discouraged because it depends on [ax-13]. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 20-Sep-2018.) (New usage is discouraged.)

Hypothesis
sb5rf.1
\( \vdash \Finv y \, \varphi \)
Conclusion
\( \vdash \varphi \leftrightarrow \exists y \, (y = x \wedge [ y / x ] \, \varphi) \)
Proof
l0
sb5rf.1
sbequ12r
equsex l0 _
bicomi _