Metamath Proof Explorer

Theorem an32

Description: A rearrangement of conjuncts. (Contributed by NM, 12-Mar-1995) (Proof shortened by Wolf Lammen, 25-Dec-2012)

Ref Expression
Assertion an32 
|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )

Proof

Step Hyp Ref Expression
1 an21 
 |-  ( ( ( ph /\ ps ) /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )
2 1 biancomi 
 |-  ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )