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  1192  3anbi2i  1193  3anbi3i  1194  trubitru  1426  falbifal  1429  eqid  2193  abid2  2314  abid2f  2362  ceqsexg  2889  nnwetri  6974  exmidontriimlem3  7285  fsum2d  11581  fprod2d  11769  isstructim  12635  lmodvscl  13804  lgsquad2  15240