Theorem bj-ssbid2

Description: A special case of sbequ2 . (Contributed by BJ, 22-Dec-2020)

	Ref	Expression
Assertion	bj-ssbid2	⊢ ( [ 𝑥 / 𝑥 ] 𝜑 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		equid	⊢ 𝑥 = 𝑥
2		sbequ2	⊢ ( 𝑥 = 𝑥 → ( [ 𝑥 / 𝑥 ] 𝜑 → 𝜑 ) )
3	1 2	ax-mp	⊢ ( [ 𝑥 / 𝑥 ] 𝜑 → 𝜑 )