Theorem an2anr

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

	Ref	Expression
Assertion	an2anr	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜓 ∧ 𝜑 ) ∧ ( 𝜃 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ancom	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜓 ∧ 𝜑 ) )
2		ancom	⊢ ( ( 𝜒 ∧ 𝜃 ) ↔ ( 𝜃 ∧ 𝜒 ) )
3	1 2	anbi12i	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜓 ∧ 𝜑 ) ∧ ( 𝜃 ∧ 𝜒 ) ) )