Metamath Proof Explorer


Theorem ad2antrl

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999)

Ref Expression
Hypothesis ad2ant.1 ⊢ ( 𝜑 → 𝜓 )
Assertion ad2antrl ( ( 𝜒 ∧ ( 𝜑 ∧ 𝜃 ) ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 ad2ant.1 ⊢ ( 𝜑 → 𝜓 )
2 1 adantl ⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜓 )
3 2 adantrr ⊢ ( ( 𝜒 ∧ ( 𝜑 ∧ 𝜃 ) ) → 𝜓 )