Theorem pm4.38 569

Description: Theorem *4.38 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)

Assertion

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

Proof of Theorem pm4.38

Step	Hyp	Ref	Expression
1		simpl 107	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ph <-> ch ) )
2		simpr 108	. 2 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ps <-> th ) )
3	1, 2	anbi12d 456	1 |- ( ( ( ph <-> ch ) /\ ( ps <-> th ) ) -> ( ( ph /\ ps ) <-> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  isprm3  10500