Theorem bj-genl

Description: Generalization rule on the left conjunct. See 19.27 . (Contributed by BJ, 7-Jul-2021)

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

Proof

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