Metamath Proof Explorer


Theorem 3adant3l

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 25-Jun-2022)

Ref Expression
Hypothesis ad4ant3.1 ( ( 𝜑𝜓𝜒 ) → 𝜃 )
Assertion 3adant3l ( ( 𝜑𝜓 ∧ ( 𝜏𝜒 ) ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 ad4ant3.1 ( ( 𝜑𝜓𝜒 ) → 𝜃 )
2 simpr ( ( 𝜏𝜒 ) → 𝜒 )
3 2 1 syl3an3 ( ( 𝜑𝜓 ∧ ( 𝜏𝜒 ) ) → 𝜃 )