Theorem pm4.22 622

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

Assertion

Ref	Expression
pm4.22	|- (((ph <-> ps) /\ (ps <-> ch)) -> (ph <-> ch))

Proof of Theorem pm4.22

Step	Hyp	Ref	Expression
1		id 59	. . 3 |- ((ph <-> ps) -> (ph <-> ps))
2	1	bibi1d 619	. 2 |- ((ph <-> ps) -> ((ph <-> ch) <-> (ps <-> ch)))
3	2	biimpar 417	1 |- (((ph <-> ps) /\ (ps <-> ch)) -> (ph <-> ch))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

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 147  df-an 225

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