Metamath Proof Explorer

Theorem pm4.38

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

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

Proof

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