Theorem adantrd

Description: Deduction adding a conjunct to the right of an antecedent. (Contributed by NM, 4-May-1994)

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

Proof

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