Theorem 3an1rs

Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007) (Proof shortened by Wolf Lammen, 14-Apr-2022)

	Ref	Expression
Hypothesis	3an1rs.1	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$
Assertion	3an1rs	$$⊢\left(\left(\phi \wedge \psi \wedge \theta \right)\wedge \chi \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		3an1rs.1	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$
2	1	3exp1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
3	2	com34	$$⊢\phi \to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)$$
4	3	3imp1	$$⊢\left(\left(\phi \wedge \psi \wedge \theta \right)\wedge \chi \right)\to \tau$$