Theorem biid

Description: Principle of identity for logical equivalence. Theorem *4.2 of WhiteheadRussell p. 117. This is part of Frege's eighth axiom per Proposition 54 of Frege1879 p. 50; see also eqid . (Contributed by NM, 2-Jun-1993)

	Ref	Expression
Assertion	biid	⊢ ( 𝜑 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝜑 → 𝜑 )
2	1 1	impbii	⊢ ( 𝜑 ↔ 𝜑 )