Theorem sbidd-misc

Description: An identity theorem for substitution. See sbid . See Remark 9.1 in Megill p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017)

	Ref	Expression
Assertion	sbidd-misc	|- ( ( ph -> [ x / x ] ps ) <-> ( ph -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		sbid	|- ( [ x / x ] ps <-> ps )
2	1	imbi2i	|- ( ( ph -> [ x / x ] ps ) <-> ( ph -> ps ) )