Metamath Proof Explorer

Theorem an13

Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012) (Proof shortened by Wolf Lammen, 31-Dec-2012)

Ref Expression
Assertion an13 
|- ( ( ph /\ ( ps /\ ch ) ) <-> ( ch /\ ( ps /\ ph ) ) )

Proof

Step Hyp Ref Expression
1 an21 
 |-  ( ( ( ps /\ ph ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2 ancom 
 |-  ( ( ( ps /\ ph ) /\ ch ) <-> ( ch /\ ( ps /\ ph ) ) )
3 1 2 bitr3i 
 |-  ( ( ph /\ ( ps /\ ch ) ) <-> ( ch /\ ( ps /\ ph ) ) )