Theorem bitr 469

Description: Theorem *4.22 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
bitr	|- ( ( ( ph <-> ps ) /\ ( ps <-> ch ) ) -> ( ph <-> ch ) )

Proof of Theorem bitr

Step	Hyp	Ref	Expression
1		bibi1 239	. 2 |- ( ( ph <-> ps ) -> ( ( ph <-> ch ) <-> ( ps <-> ch ) ) )
2	1	biimpar 295	1 |- ( ( ( ph <-> ps ) /\ ( ps <-> ch ) ) -> ( ph <-> ch ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> 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:  opelopabt  4247