Theorem adantld

Description: Deduction adding a conjunct to the left of an antecedent. (Contributed by NM, 4-May-1994) (Proof shortened by Wolf Lammen, 20-Dec-2012)

	Ref	Expression
Hypothesis	adantld.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	adantld	$$⊢\phi \to \left(\left(\theta \wedge \psi \right)\to \chi \right)$$

Proof

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