Theorem 3adant1

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995) (Proof shortened by Wolf Lammen, 21-Jun-2022)

	Ref	Expression
Hypothesis	3adant.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	3adant1	⊢ ( ( 𝜃 ∧ 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		3adant.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2	1	adantll	⊢ ( ( ( 𝜃 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )
3	2	3impa	⊢ ( ( 𝜃 ∧ 𝜑 ∧ 𝜓 ) → 𝜒 )