Theorem simpl2im

Description: Implication from an eliminated conjunct implied by the antecedent. (Contributed by BJ/AV, 5-Apr-2021) (Proof shortened by Wolf Lammen, 26-Mar-2022)

	Ref	Expression
Hypotheses	simpl2im.1	$$⊢\phi \to \left(\psi \wedge \chi \right)$$
	simpl2im.2	$$⊢\chi \to \theta$$
Assertion	simpl2im	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		simpl2im.1	$$⊢\phi \to \left(\psi \wedge \chi \right)$$
2		simpl2im.2	$$⊢\chi \to \theta$$
3	1	simprd	$$⊢\phi \to \chi$$
4	3 2	syl	$$⊢\phi \to \theta$$