Theorem bitr 684

Description: Theorem *4.22 of [WhiteheadRussell] p. 117.

Assertion

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

Proof of Theorem bitr

Step	Hyp	Ref	Expression
1		id 73	. . 3 |- ((ph <-> ps) -> (ph <-> ps))
2	1	bibi1d 681	. 2 |- ((ph <-> ps) -> ((ph <-> ch) <-> (ps <-> ch)))
3	2	biimpar 461	1 |- (((ph <-> ps) /\ (ps <-> ch)) -> (ph <-> ch))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240

This theorem is referenced by:  absdvdsb 13673  dvdsabsb 13674  albitr 16310  3orbi123VD 16674

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

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