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  1217  3anbi2i  1218  3anbi3i  1219  trubitru  1460  falbifal  1463  eqid  2234  abid2  2357  abid1  2368  abid2f  2412  ceqsexg  2948  nnwetri  7189  isacnm  7523  exmidontriimlem3  7543  fsum2d  12146  fprod2d  12334  isstructim  13310  lmodvscl  14579  lgsquad2  16082  clwwlkccat  16522