Theorem frege58bcor

Description: Lemma for frege59b . (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege58bcor	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( [ 𝑦 / 𝑥 ] 𝜑 → [ 𝑦 / 𝑥 ] 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege58b	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → [ 𝑦 / 𝑥 ] ( 𝜑 → 𝜓 ) )
2		sbim	⊢ ( [ 𝑦 / 𝑥 ] ( 𝜑 → 𝜓 ) ↔ ( [ 𝑦 / 𝑥 ] 𝜑 → [ 𝑦 / 𝑥 ] 𝜓 ) )
3	1 2	sylib	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( [ 𝑦 / 𝑥 ] 𝜑 → [ 𝑦 / 𝑥 ] 𝜓 ) )