Theorem spsbbiOLD

Description: Obsolete version of spsbbi as of 6-Jul-2023. Specialization of biconditional. (Contributed by NM, 2-Jun-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	spsbbiOLD	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ 𝑦 / 𝑥 ] 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		stdpc4	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → [ 𝑦 / 𝑥 ] ( 𝜑 ↔ 𝜓 ) )
2		sbbi	⊢ ( [ 𝑦 / 𝑥 ] ( 𝜑 ↔ 𝜓 ) ↔ ( [ 𝑦 / 𝑥 ] 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜓 ) )
3	1 2	sylib	⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( [ 𝑦 / 𝑥 ] 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜓 ) )