Metamath Proof Explorer


Theorem ad4antr

Description: Deduction adding 4 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 ad4antr ( ( ( ( ( 𝜑𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 ad2ant.1 ( 𝜑𝜓 )
2 1 adantr ( ( 𝜑𝜒 ) → 𝜓 )
3 2 ad3antrrr ( ( ( ( ( 𝜑𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) → 𝜓 )