Theorem als2d

Description: Deduction rule: Given "all some" applied to a top-level inference, you can extract the "exists" part. (Contributed by David A. Wheeler, 20-Oct-2018)

	Ref	Expression
Hypothesis	als2d.1	No typesetting found for |- ( ph -> AE x ( ps -> ch ) ) with typecode |-
Assertion	als2d	$$⊢\phi \to \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		als2d.1	Could not format ( ph -> AE x ( ps -> ch ) ) : No typesetting found for |- ( ph -> AE x ( ps -> ch ) ) with typecode |-
2		df-als	Could not format ( AE x ( ps -> ch ) <-> ( A. x ( ps -> ch ) /\ E. x ps ) ) : No typesetting found for |- ( AE x ( ps -> ch ) <-> ( A. x ( ps -> ch ) /\ E. x ps ) ) with typecode |-
3	1 2	sylib	$$⊢\phi \to \left(\forall x\left(\psi \to \chi \right)\wedge \exists x\psi \right)$$
4	3	simprd	$$⊢\phi \to \exists x\psi$$