Theorem biid 170

Description: Principle of identity for logical equivalence. Theorem *4.2 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
biid	⊢ (𝜑 ↔ 𝜑)

Proof of Theorem biid

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝜑 → 𝜑)
2	1, 1	impbii 125	1 ⊢ (𝜑 ↔ 𝜑)

Syntax hints:   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  biidd  171  3anbi1i  1173  3anbi2i  1174  3anbi3i  1175  trubitru  1397  falbifal  1400  eqid  2157  abid2  2278  abid2f  2325  ceqsexg  2840  nnwetri  6860  exmidontriimlem3  7158  fsum2d  11332  fprod2d  11520  isstructim  12215