Theorem adantr

Description: Inference adding a conjunct to the right of an antecedent. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	adantr.1	⊢ ( 𝜑 → 𝜓 )
Assertion	adantr	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		adantr.1	⊢ ( 𝜑 → 𝜓 )
2	1	a1d	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )
3	2	imp	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 )