Theorem ad8antr

Description: Deduction adding 8 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)

	Ref	Expression
Hypothesis	ad2ant.1	⊢ ( 𝜑 → 𝜓 )
Assertion	ad8antr	⊢ ( ( ( ( ( ( ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ad2ant.1	⊢ ( 𝜑 → 𝜓 )
2	1	adantr	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 )
3	2	ad7antr	⊢ ( ( ( ( ( ( ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) → 𝜓 )