Metamath Proof Explorer


Theorem ad6antlr

Description: Deduction adding 6 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)

Ref Expression
Hypothesis ad2ant.1 ( 𝜑𝜓 )
Assertion ad6antlr ( ( ( ( ( ( ( 𝜒𝜑 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 ad2ant.1 ( 𝜑𝜓 )
2 1 adantl ( ( 𝜒𝜑 ) → 𝜓 )
3 2 ad5antr ( ( ( ( ( ( ( 𝜒𝜑 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) → 𝜓 )