Theorem bj-genr

Description: Generalization rule on the right conjunct. See 19.28 . (Contributed by BJ, 7-Jul-2021)

	Ref	Expression
Hypothesis	bj-genr.1	$$⊢\left(\phi \wedge \psi \right)$$
Assertion	bj-genr	$$⊢\left(\phi \wedge \forall x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-genr.1	$$⊢\left(\phi \wedge \psi \right)$$
2	1	simpli	$$⊢\phi$$
3	1	simpri	$$⊢\psi$$
4	3	ax-gen	$$⊢\forall x\psi$$
5	2 4	pm3.2i	$$⊢\left(\phi \wedge \forall x\psi \right)$$