Theorem frege53aid 45002

Description: Specialization of frege53a 45003. Proposition 53 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege53aid

Step	Hyp	Ref	Expression
1		frege52aid 45001	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓))
2		ax-frege8 44952	. 2 ⊢ (((𝜑 ↔ 𝜓) → (𝜑 → 𝜓)) → (𝜑 → ((𝜑 ↔ 𝜓) → 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (𝜑 → ((𝜑 ↔ 𝜓) → 𝜓))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 44952  ax-frege52a 45000

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ifp 1079  df-tru 1572  df-fal 1582

This theorem is used by: (None)