Theorem uun121p1

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	uun121p1.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \phi \right)\to \chi$$
Assertion	uun121p1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		uun121p1.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \phi \right)\to \chi$$
2		anabs1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \phi \right)\leftrightarrow \left(\phi \wedge \psi \right)$$
3	2 1	sylbir	$$⊢\left(\phi \wedge \psi \right)\to \chi$$