Theorem adantll

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Hypothesis	adant2.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	adantll	⊢ ( ( ( 𝜃 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		adant2.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2		simpr	⊢ ( ( 𝜃 ∧ 𝜑 ) → 𝜑 )
3	2 1	sylan	⊢ ( ( ( 𝜃 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )