Theorem un01

Description: A unionizing deduction. (Contributed by Alan Sare, 28-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	un01.1	$$⊢\left(\left(\top ,\phi \right)\to \psi \right)$$
Assertion	un01	$$⊢\left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		un01.1	$$⊢\left(\left(\top ,\phi \right)\to \psi \right)$$
2		tru	$$⊢\top$$
3	2	jctl	$$⊢\phi \to \left(\top \wedge \phi \right)$$
4	1	dfvd2ani	$$⊢\left(\top \wedge \phi \right)\to \psi$$
5	3 4	syl	$$⊢\phi \to \psi$$
6	5	dfvd1ir	$$⊢\left(\phi \to \psi \right)$$