Theorem an12i

Description: An inference from commuting operands in a chain of conjunctions. (Contributed by Giovanni Mascellani, 22-May-2019)

	Ref	Expression
Hypothesis	an12i.1	⊢ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) )
Assertion	an12i	⊢ ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		an12i.1	⊢ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) )
2		an12	⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) )
3	1 2	mpbir	⊢ ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) )