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	⊢ ( ( 𝜑 → [ 𝑥 / 𝑥 ] 𝜓 ) ↔ ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		sbid	⊢ ( [ 𝑥 / 𝑥 ] 𝜓 ↔ 𝜓 )
2	1	imbi2i	⊢ ( ( 𝜑 → [ 𝑥 / 𝑥 ] 𝜓 ) ↔ ( 𝜑 → 𝜓 ) )