Theorem impel

Description: An inference for implication elimination. (Contributed by Giovanni Mascellani, 23-May-2019) (Proof shortened by Wolf Lammen, 2-Sep-2020)

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

Proof

Step	Hyp	Ref	Expression
1		impel.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		impel.2	$$⊢\theta \to \psi$$
3	2 1	syl5	$$⊢\phi \to \left(\theta \to \chi \right)$$
4	3	imp	$$⊢\left(\phi \wedge \theta \right)\to \chi$$