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	|- ( ph <-> ph )

Proof of Theorem biid

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ph -> ph )
2	1, 1	impbii 126	1 |- ( ph <-> ph )

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  1193  3anbi2i  1194  3anbi3i  1195  trubitru  1435  falbifal  1438  eqid  2205  abid2  2326  abid2f  2374  ceqsexg  2901  nnwetri  7015  isacnm  7317  exmidontriimlem3  7337  fsum2d  11779  fprod2d  11967  isstructim  12879  lmodvscl  14100  lgsquad2  15593