Theorem ad5ant125

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 23-Jun-2022)

	Ref	Expression
Hypothesis	ad5ant.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	ad5ant125	⊢ ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		ad5ant.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3expia	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
3	2	2a1d	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜏 → ( 𝜂 → ( 𝜒 → 𝜃 ) ) ) )
4	3	imp41	⊢ ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜒 ) → 𝜃 )