Theorem uun123

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	uun123.1	$$⊢\left(\phi \wedge \chi \wedge \psi \right)\to \theta$$
Assertion	uun123	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		uun123.1	$$⊢\left(\phi \wedge \chi \wedge \psi \right)\to \theta$$
2		3ancomb	$$⊢\left(\phi \wedge \chi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \psi \wedge \chi \right)$$
3	2 1	sylbir	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$