Theorem adantrd

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

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

Proof

Step	Hyp	Ref	Expression
1		adantrd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		simpl	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜓 )
3	2 1	syl5	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜃 ) → 𝜒 ) )