Theorem sb6rf

Reversed substitution. For a version requiring disjoint variables, but fewer axioms, see sb6rfv. Usage of this theorem is discouraged because it depends on [ax-13]. Use the weaker sb6rfv if possible. (Contributed by NM, 1-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 21-Sep-2018.) (New usage is discouraged.)

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