Theorem an4com24

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

	Ref	Expression
Assertion	an4com24	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜒 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		an43	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜓 ∧ 𝜒 ) ) )
2		ancom	⊢ ( ( 𝜓 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ) )
3	2	anbi2i	⊢ ( ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜓 ∧ 𝜒 ) ) ↔ ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜒 ∧ 𝜓 ) ) )
4	1 3	bitri	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜃 ) ∧ ( 𝜒 ∧ 𝜓 ) ) )