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Metamath Proof Explorer

Theorem sbcovOLD

Description: Obsolete version of sbcov as of 26-Aug-2025. (Contributed by NM, 14-May-1993) (Revised by GG, 7-Aug-2023) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	sbcovOLD	⊢ ( [ 𝑦 / 𝑥 ] [ 𝑥 / 𝑦 ] 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		sbcom3vv	⊢ ( [ 𝑦 / 𝑥 ] [ 𝑥 / 𝑦 ] 𝜑 ↔ [ 𝑦 / 𝑥 ] [ 𝑦 / 𝑦 ] 𝜑 )
2		sbid	⊢ ( [ 𝑦 / 𝑦 ] 𝜑 ↔ 𝜑 )
3	2	sbbii	⊢ ( [ 𝑦 / 𝑥 ] [ 𝑦 / 𝑦 ] 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜑 )
4	1 3	bitri	⊢ ( [ 𝑦 / 𝑥 ] [ 𝑥 / 𝑦 ] 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜑 )