Theorem 3adant2l

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 25-Jun-2022)

	Ref	Expression
Hypothesis	ad4ant3.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	3adant2l	⊢ ( ( 𝜑 ∧ ( 𝜏 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2		simpr	⊢ ( ( 𝜏 ∧ 𝜓 ) → 𝜓 )
3	2 1	syl3an2	⊢ ( ( 𝜑 ∧ ( 𝜏 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )