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Metamath Proof Explorer

Theorem bj-ssbid1

Description: A special case of sbequ1 . (Contributed by BJ, 22-Dec-2020)

		Ref	Expression
	Assertion	bj-ssbid1	⊢ ( 𝜑 → [ 𝑥 / 𝑥 ] 𝜑 )

Step	Hyp	Ref	Expression
1		equid	⊢ 𝑥 = 𝑥
2		sbequ1	⊢ ( 𝑥 = 𝑥 → ( 𝜑 → [ 𝑥 / 𝑥 ] 𝜑 ) )
3	1 2	ax-mp	⊢ ( 𝜑 → [ 𝑥 / 𝑥 ] 𝜑 )