Theorem sbidd

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
Hypothesis	sbidd.1	⊢ ( 𝜑 → [ 𝑥 / 𝑥 ] 𝜓 )
Assertion	sbidd	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		sbidd.1	⊢ ( 𝜑 → [ 𝑥 / 𝑥 ] 𝜓 )
2		sbid	⊢ ( [ 𝑥 / 𝑥 ] 𝜓 ↔ 𝜓 )
3	1 2	sylib	⊢ ( 𝜑 → 𝜓 )