Theorem bicom 139

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 130	. 2 |- ( ( ph <-> ps ) -> ( ps <-> ph ) )
2		bicom1 130	. 2 |- ( ( ps <-> ph ) -> ( ph <-> ps ) )
3	1, 2	impbii 125	1 |- ( ( ph <-> ps ) <-> ( ps <-> ph ) )

Syntax hints:   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  bicomd  140  bibi1i  227  bibi1d  232  ibibr  245  bibif  688  con2bidc  865  con2biddc  870  pm5.17dc  894  bigolden  944  nbbndc  1383  bilukdc  1385  falbitru  1406  3impexpbicom  1425  exists1  2109  eqcom  2166  abeq1  2274  necon2abiddc  2400  necon2bbiddc  2401  necon4bbiddc  2408  ssequn1  3287  axpow3  4150  isocnv  5773  suplocsrlem  7740  uzennn  10361  bezoutlemle  11926