Theorem bj-sylget

Description: Dual statement of sylgt . Closed form of bj-sylge . (Contributed by BJ, 2-May-2019)

	Ref	Expression
Assertion	bj-sylget	$$⊢\forall x\left(\chi \to \phi \right)\to \left(\left(\exists x\phi \to \psi \right)\to \left(\exists x\chi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		exim	$$⊢\forall x\left(\chi \to \phi \right)\to \left(\exists x\chi \to \exists x\phi \right)$$
2	1	imim1d	$$⊢\forall x\left(\chi \to \phi \right)\to \left(\left(\exists x\phi \to \psi \right)\to \left(\exists x\chi \to \psi \right)\right)$$