Theorem bnj31

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj31.1	$$⊢\phi \to \exists x\in A\psi$$
	bnj31.2	$$⊢\psi \to \chi$$
Assertion	bnj31	$$⊢\phi \to \exists x\in A\chi$$

Proof

Step	Hyp	Ref	Expression
1		bnj31.1	$$⊢\phi \to \exists x\in A\psi$$
2		bnj31.2	$$⊢\psi \to \chi$$
3	2	reximi	$$⊢\exists x\in A\psi \to \exists x\in A\chi$$
4	1 3	syl	$$⊢\phi \to \exists x\in A\chi$$