Metamath Proof Explorer


Theorem adantrlr

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

Ref Expression
Hypothesis adantr2.1 ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → 𝜃 )
Assertion adantrlr ( ( 𝜑 ∧ ( ( 𝜓𝜏 ) ∧ 𝜒 ) ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 adantr2.1 ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → 𝜃 )
2 simpl ( ( 𝜓𝜏 ) → 𝜓 )
3 2 1 sylanr1 ( ( 𝜑 ∧ ( ( 𝜓𝜏 ) ∧ 𝜒 ) ) → 𝜃 )