Theorem 19.33

Description: Theorem 19.33 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Assertion	19.33	$$⊢\left(\forall x\phi \vee \forall x\psi \right)\to \forall x\left(\phi \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orc	$$⊢\phi \to \left(\phi \vee \psi \right)$$
2	1	alimi	$$⊢\forall x\phi \to \forall x\left(\phi \vee \psi \right)$$
3		olc	$$⊢\psi \to \left(\phi \vee \psi \right)$$
4	3	alimi	$$⊢\forall x\psi \to \forall x\left(\phi \vee \psi \right)$$
5	2 4	jaoi	$$⊢\left(\forall x\phi \vee \forall x\psi \right)\to \forall x\left(\phi \vee \psi \right)$$