Metamath Proof Explorer


Theorem ad5ant13

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

Ref Expression
Hypothesis ad5ant2.1 ( ( 𝜑𝜓 ) → 𝜒 )
Assertion ad5ant13 ( ( ( ( ( 𝜑𝜃 ) ∧ 𝜓 ) ∧ 𝜏 ) ∧ 𝜂 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 ad5ant2.1 ( ( 𝜑𝜓 ) → 𝜒 )
2 1 adantlr ( ( ( 𝜑𝜃 ) ∧ 𝜓 ) → 𝜒 )
3 2 ad2antrr ( ( ( ( ( 𝜑𝜃 ) ∧ 𝜓 ) ∧ 𝜏 ) ∧ 𝜂 ) → 𝜒 )