Theorem sbid2v

An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). Usage of this theorem is discouraged because it depends on [ax-13]. See sbid2vw for a version with an extra disjoint variable condition requiring fewer axioms. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Conclusion
\( \vdash [ y / x ] \, [ x / y ] \, \varphi \leftrightarrow \varphi \)
Proof
nfv
sbid2 _