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  1216  3anbi2i  1217  3anbi3i  1218  trubitru  1459  falbifal  1462  eqid  2231  abid2  2352  abid2f  2400  ceqsexg  2934  nnwetri  7107  isacnm  7417  exmidontriimlem3  7437  fsum2d  11995  fprod2d  12183  isstructim  13095  lmodvscl  14318  lgsquad2  15811  clwwlkccat  16251