Metamath Proof Explorer


Theorem ad9antr

Description: Deduction adding 9 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)

Ref Expression
Hypothesis ad2ant.1 ( 𝜑𝜓 )
Assertion ad9antr ( ( ( ( ( ( ( ( ( ( 𝜑𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 ad2ant.1 ( 𝜑𝜓 )
2 1 adantr ( ( 𝜑𝜒 ) → 𝜓 )
3 2 ad8antr ( ( ( ( ( ( ( ( ( ( 𝜑𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) → 𝜓 )