Theorem bibi1 239

Description: Theorem *4.86 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
bibi1	|- ( ( ph <-> ps ) -> ( ( ph <-> ch ) <-> ( ps <-> ch ) ) )

Proof of Theorem bibi1

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph <-> ps ) -> ( ph <-> ps ) )
2	1	bibi1d 232	1 |- ( ( ph <-> ps ) -> ( ( ph <-> ch ) <-> ( ps <-> ch ) ) )

Syntax hints:   -> wi 4   <-> 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:  bitr  464  pm5.18im  1375  sbeqalb  3006