Theorem bj-sylge

Description: Dual statement of sylg (the final "e" in the label stands for "existential (version of sylg )". Variant of exlimih . (Contributed by BJ, 25-Dec-2023)

	Ref	Expression
Hypotheses	bj-sylge.nf	$$⊢\exists x\phi \to \psi$$
	bj-sylge.maj	$$⊢\chi \to \phi$$
Assertion	bj-sylge	$$⊢\exists x\chi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-sylge.nf	$$⊢\exists x\phi \to \psi$$
2		bj-sylge.maj	$$⊢\chi \to \phi$$
3	2	eximi	$$⊢\exists x\chi \to \exists x\phi$$
4	3 1	syl	$$⊢\exists x\chi \to \psi$$