Theorem pm4.38 631

Description: Theorem *4.38 of [WhiteheadRussell] p. 118.

Assertion

Ref	Expression
pm4.38	|- (((ph <-> ch) /\ (ps <-> th)) -> ((ph /\ ps) <-> (ch /\ th)))

Proof of Theorem pm4.38

Step	Hyp	Ref	Expression
1		pm3.26 319	. 2 |- (((ph <-> ch) /\ (ps <-> th)) -> (ph <-> ch))
2		pm3.27 323	. 2 |- (((ph <-> ch) /\ (ps <-> th)) -> (ps <-> th))
3	1, 2	anbi12d 628	1 |- (((ph <-> ch) /\ (ps <-> th)) -> ((ph /\ ps) <-> (ch /\ th)))

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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