Theorem 3impcombi

Description: A 1-hypothesis propositional calculus deduction. (Contributed by Alan Sare, 25-Sep-2017)

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

Proof

Step	Hyp	Ref	Expression
1		3impcombi.1	$$⊢\left(\phi \wedge \psi \wedge \phi \right)\to \left(\chi \leftrightarrow \theta \right)$$
2	1	biimpd	$$⊢\left(\phi \wedge \psi \wedge \phi \right)\to \left(\chi \to \theta \right)$$
3	2	3anidm13	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
4	3	ancoms	$$⊢\left(\psi \wedge \phi \right)\to \left(\chi \to \theta \right)$$
5	4	3impia	$$⊢\left(\psi \wedge \phi \wedge \chi \right)\to \theta$$