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	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		an42	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜓 ) ) )
2		3an4anass	⊢ ( ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ ( 𝜃 ∧ 𝜓 ) ) )
3	1 2	bitr4i	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) )