Theorem ad5ant245

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 14-Apr-2022)

	Ref	Expression
Hypothesis	ad5ant.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	ad5ant245	⊢ ( ( ( ( ( 𝜏 ∧ 𝜑 ) ∧ 𝜂 ) ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		ad5ant.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3adant1l	⊢ ( ( ( 𝜏 ∧ 𝜑 ) ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
3	2	ad4ant134	⊢ ( ( ( ( ( 𝜏 ∧ 𝜑 ) ∧ 𝜂 ) ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )