Theorem 3ad2antl3

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007)

	Ref	Expression
Hypothesis	3ad2antl.1	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
Assertion	3ad2antl3	⊢ ( ( ( 𝜓 ∧ 𝜏 ∧ 𝜑 ) ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3ad2antl.1	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
2	1	adantll	⊢ ( ( ( 𝜏 ∧ 𝜑 ) ∧ 𝜒 ) → 𝜃 )
3	2	3adantl1	⊢ ( ( ( 𝜓 ∧ 𝜏 ∧ 𝜑 ) ∧ 𝜒 ) → 𝜃 )