Metamath Proof Explorer

Theorem an2anr

Description: Double commutation in conjunction. (Contributed by Peter Mazsa, 27-Jun-2019)

Ref Expression
Assertion an2anr 
|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ps /\ ph ) /\ ( th /\ ch ) ) )

Proof

Step Hyp Ref Expression
1 ancom 
 |-  ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2 ancom 
 |-  ( ( ch /\ th ) <-> ( th /\ ch ) )
3 1 2 anbi12i 
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ps /\ ph ) /\ ( th /\ ch ) ) )