Theorem frege55aid 44619

Description: Lemma for frege57aid 44626. Core proof of Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
frege55aid	⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑))

Proof of Theorem frege55aid

Step	Hyp	Ref	Expression
1		bicom1 224	1 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑))

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

This proof depends on definitions:  df-bi 210

This theorem is used by:  frege56aid  44624