Metamath Proof Explorer

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


Step Hyp Ref Expression
1 id φ φ
2 1 1 impbii φ φ