Theorem bicom 140

Description: Commutative law for equivalence. Theorem *4.21 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 11-Nov-2012.)

Assertion

Ref	Expression
bicom	|- ( ( ph <-> ps ) <-> ( ps <-> ph ) )

Proof of Theorem bicom

Step	Hyp	Ref	Expression
1		bicom1 131	. 2 |- ( ( ph <-> ps ) -> ( ps <-> ph ) )
2		bicom1 131	. 2 |- ( ( ps <-> ph ) -> ( ph <-> ps ) )
3	1, 2	impbii 126	1 |- ( ( ph <-> ps ) <-> ( ps <-> ph ) )

Syntax hints:   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  bicomd  141  bibi1i  228  bibi1d  233  ibibr  246  bibif  699  con2bidc  876  con2biddc  881  pm5.17dc  905  bigolden  957  nbbndc  1405  bilukdc  1407  falbitru  1428  3impexpbicom  1449  exists1  2134  eqcom  2191  abeq1  2299  necon2abiddc  2426  necon2bbiddc  2427  necon4bbiddc  2434  ssequn1  3320  axpow3  4195  isocnv  5833  suplocsrlem  7838  uzennn  10469  bezoutlemle  12044