Metamath Proof Explorer

Theorem an4

Description: Rearrangement of 4 conjuncts. (Contributed by NM, 10-Jul-1994)

Ref Expression
Assertion an4 
|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ th ) ) )

Proof

Step Hyp Ref Expression
1 anass 
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ph /\ ( ps /\ ( ch /\ th ) ) ) )
2 an12 
 |-  ( ( ps /\ ( ch /\ th ) ) <-> ( ch /\ ( ps /\ th ) ) )
3 2 bianass 
 |-  ( ( ph /\ ( ps /\ ( ch /\ th ) ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ th ) ) )
4 1 3 bitri 
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ th ) ) )