Theorem frege53aid

Description: Specialization of frege53a . Proposition 53 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege53aid	⊢ ( 𝜑 → ( ( 𝜑 ↔ 𝜓 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		frege52aid	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 → 𝜓 ) )
2		ax-frege8	⊢ ( ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 → 𝜓 ) ) → ( 𝜑 → ( ( 𝜑 ↔ 𝜓 ) → 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( 𝜑 → ( ( 𝜑 ↔ 𝜓 ) → 𝜓 ) )