Metamath Proof Explorer


Theorem adantlrl

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

Ref Expression
Hypothesis adantl2.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion adantlrl ( ( ( 𝜑 ∧ ( 𝜏𝜓 ) ) ∧ 𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 adantl2.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
2 simpr ( ( 𝜏𝜓 ) → 𝜓 )
3 2 1 sylanl2 ( ( ( 𝜑 ∧ ( 𝜏𝜓 ) ) ∧ 𝜒 ) → 𝜃 )