Theorem 4anpull2

Description: An equivalence of two four-terms conjunctions with the terms regrouped (here, the second sub-conjunct of the first term is pulled separately). (Contributed by Zhi Wang, 4-Sep-2024) (Proof shortened by Garrett Katz, 26-Jun-2026)

	Ref	Expression
Assertion	4anpull2	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch /\ th ) /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		an42	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )
2		3an4anass	|- ( ( ( ph /\ ch /\ th ) /\ ps ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )
3	1 2	bitr4i	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch /\ th ) /\ ps ) )