Theorem biid 171

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 126	1 ⊢ (𝜑 ↔ 𝜑)

Syntax hints:   ↔ wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  biidd  172  an21  471  3anbi1i  1217  3anbi2i  1218  3anbi3i  1219  trubitru  1460  falbifal  1463  eqid  2231  abid2  2353  abid2f  2401  ceqsexg  2935  nnwetri  7151  isacnm  7461  exmidontriimlem3  7481  fsum2d  12059  fprod2d  12247  isstructim  13159  lmodvscl  14384  lgsquad2  15885  clwwlkccat  16325