Metamath Proof Explorer


Theorem 3adantl1

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005)

Ref Expression
Hypothesis 3adantl.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion 3adantl1 ( ( ( 𝜏𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 3adantl.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
2 3simpc ( ( 𝜏𝜑𝜓 ) → ( 𝜑𝜓 ) )
3 2 1 sylan ( ( ( 𝜏𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )