Metamath Proof Explorer


Theorem 3ad2antr2

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 27-Dec-2007)

Ref Expression
Hypothesis 3ad2antl.1 ( ( 𝜑𝜒 ) → 𝜃 )
Assertion 3ad2antr2 ( ( 𝜑 ∧ ( 𝜓𝜒𝜏 ) ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 3ad2antl.1 ( ( 𝜑𝜒 ) → 𝜃 )
2 1 adantrl ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → 𝜃 )
3 2 3adantr3 ( ( 𝜑 ∧ ( 𝜓𝜒𝜏 ) ) → 𝜃 )