Metamath Proof Explorer


Theorem ad2ant2l

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 8-Jan-2006)

Ref Expression
Hypothesis ad2ant2.1 ( ( 𝜑𝜓 ) → 𝜒 )
Assertion ad2ant2l ( ( ( 𝜃𝜑 ) ∧ ( 𝜏𝜓 ) ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 ad2ant2.1 ( ( 𝜑𝜓 ) → 𝜒 )
2 1 adantrl ( ( 𝜑 ∧ ( 𝜏𝜓 ) ) → 𝜒 )
3 2 adantll ( ( ( 𝜃𝜑 ) ∧ ( 𝜏𝜓 ) ) → 𝜒 )