Theorem 3com12

Description: Commutation in antecedent. Swap 1st and 2nd. (Contributed by NM, 28-Jan-1996) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 22-Jun-2022)

	Ref	Expression
Hypothesis	3exp.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	3com12	$$⊢\left(\psi \wedge \phi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3exp.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2	1	3exp	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	3imp21	$$⊢\left(\psi \wedge \phi \wedge \chi \right)\to \theta$$