Theorem bibi1 341

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 22	. 2 |- ( ( ph <-> ps ) -> ( ph <-> ps ) )
2	1	bibi1d 333	1 |- ( ( ph <-> ps ) -> ( ( ph <-> ch ) <-> ( ps <-> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  bitr3  342  bitr  745  eqeq1d  2624  sbeqalb  3488  isclo2  20892  sbc3orgVD  39086  trsbcVD  39113  sbcssgVD  39119  csbingVD  39120  csbsngVD  39129  csbxpgVD  39130  csbrngVD  39132  csbunigVD  39134  csbfv12gALTVD  39135  e2ebindVD  39148