Theorem 3ad2ant1

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

	Ref	Expression
Hypothesis	3ad2ant.1	⊢ ( 𝜑 → 𝜒 )
Assertion	3ad2ant1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		3ad2ant.1	⊢ ( 𝜑 → 𝜒 )
2	1	adantr	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜒 )
3	2	3adant2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜒 )