Theorem sbid2v

Description: 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.)

	Ref	Expression
Assertion	sbid2v	|- ( [ y / x ] [ x / y ] ph <-> ph )

Proof

Step	Hyp	Ref	Expression
1		nfv	|- F/ x ph
2	1	sbid2	|- ( [ y / x ] [ x / y ] ph <-> ph )