Metamath Proof Explorer


Theorem ad4ant123

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 14-Apr-2022)

Ref Expression
Hypothesis ad4ant3.1 ( ( 𝜑𝜓𝜒 ) → 𝜃 )
Assertion ad4ant123 ( ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ∧ 𝜏 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 ad4ant3.1 ( ( 𝜑𝜓𝜒 ) → 𝜃 )
2 1 3expa ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
3 2 adantr ( ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ∧ 𝜏 ) → 𝜃 )