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  1180  3anbi2i  1181  3anbi3i  1182  trubitru  1405  falbifal  1408  eqid  2165  abid2  2287  abid2f  2334  ceqsexg  2854  nnwetri  6881  exmidontriimlem3  7179  fsum2d  11376  fprod2d  11564  isstructim  12408