Theorem r19.21be

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypothesis	r19.21be.1	$$⊢\phi \to \forall x\in A\psi$$
Assertion	r19.21be	$$⊢\forall x\in A\left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		r19.21be.1	$$⊢\phi \to \forall x\in A\psi$$
2	1	r19.21bi	$$⊢\left(\phi \wedge x\in A\right)\to \psi$$
3	2	expcom	$$⊢x\in A\to \left(\phi \to \psi \right)$$
4	3	rgen	$$⊢\forall x\in A\left(\phi \to \psi \right)$$