Metamath Proof Explorer


Theorem 3ad2ant1

Description: Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005)

Ref Expression
Hypothesis 3ad2ant.1 ( 𝜑𝜒 )
Assertion 3ad2ant1 ( ( 𝜑𝜓𝜃 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 3ad2ant.1 ( 𝜑𝜒 )
2 1 adantr ( ( 𝜑𝜃 ) → 𝜒 )
3 2 3adant2 ( ( 𝜑𝜓𝜃 ) → 𝜒 )