Theorem r19.21biOLD

Description: Obsolete version of r19.21bi as of 11-Jun-2023. (Contributed by NM, 20-Nov-1994) (Proof shortened by Wolf Lammen, 1-Jan-2020) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

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