Theorem 19.9d2r

Description: A deduction version of one direction of 19.9 with two variables. (Contributed by Thierry Arnoux, 30-Jan-2017)

	Ref	Expression
Hypotheses	19.9d2r.1	$$⊢\phi \to Ⅎx\psi$$
	19.9d2r.2	$$⊢\phi \to Ⅎy\psi$$
	19.9d2r.3	$$⊢\phi \to \exists x\in A\exists y\in B\psi$$
Assertion	19.9d2r	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		19.9d2r.1	$$⊢\phi \to Ⅎx\psi$$
2		19.9d2r.2	$$⊢\phi \to Ⅎy\psi$$
3		19.9d2r.3	$$⊢\phi \to \exists x\in A\exists y\in B\psi$$
4		nfv	$$⊢Ⅎy\phi$$
5	4 1 2 3	19.9d2rf	$$⊢\phi \to \psi$$