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	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)$$
Assertion	an12i	$$⊢\left(\psi \wedge \left(\phi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		an12i.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)$$
2		an12	$$⊢\left(\psi \wedge \left(\phi \wedge \chi \right)\right)\leftrightarrow \left(\phi \wedge \left(\psi \wedge \chi \right)\right)$$
3	1 2	mpbir	$$⊢\left(\psi \wedge \left(\phi \wedge \chi \right)\right)$$