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  1214  3anbi2i  1215  3anbi3i  1216  trubitru  1457  falbifal  1460  eqid  2229  abid2  2350  abid2f  2398  ceqsexg  2931  nnwetri  7089  isacnm  7396  exmidontriimlem3  7416  fsum2d  11961  fprod2d  12149  isstructim  13061  lmodvscl  14284  lgsquad2  15777  clwwlkccat  16138