Theorem bitr 689

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 317	. 2 |- ((ph <-> ps) -> ((ph <-> ch) <-> (ps <-> ch)))
2	1	biimpar 471	1 |- (((ph <-> ps) /\ (ps <-> ch)) -> (ph <-> ch))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  opelopabt  4700