Metamath Proof Explorer


Theorem 3adantr2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005)

Ref Expression
Hypothesis 3adantr.1 ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → 𝜃 )
Assertion 3adantr2 ( ( 𝜑 ∧ ( 𝜓𝜏𝜒 ) ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 3adantr.1 ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → 𝜃 )
2 3simpb ( ( 𝜓𝜏𝜒 ) → ( 𝜓𝜒 ) )
3 2 1 sylan2 ( ( 𝜑 ∧ ( 𝜓𝜏𝜒 ) ) → 𝜃 )