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	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	adantld	⊢ ( 𝜑 → ( ( 𝜃 ∧ 𝜓 ) → 𝜒 ) )

Proof

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