Metamath Proof Explorer

Theorem an4com24

Description: Rearrangement of 4 conjuncts: second and forth positions interchanged. (Contributed by AV, 18-Feb-2022)

Ref Expression
Assertion an4com24 
|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ch /\ ps ) ) )

Proof

Step Hyp Ref Expression
1 an43 
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ps /\ ch ) ) )
2 ancom 
 |-  ( ( ps /\ ch ) <-> ( ch /\ ps ) )
3 2 anbi2i 
 |-  ( ( ( ph /\ th ) /\ ( ps /\ ch ) ) <-> ( ( ph /\ th ) /\ ( ch /\ ps ) ) )
4 1 3 bitri 
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ch /\ ps ) ) )