Theorem 3adantl2

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

	Ref	Expression
Hypothesis	3adantl.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion	3adantl2	⊢ ( ( ( 𝜑 ∧ 𝜏 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3adantl.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
2		3simpb	⊢ ( ( 𝜑 ∧ 𝜏 ∧ 𝜓 ) → ( 𝜑 ∧ 𝜓 ) )
3	2 1	sylan	⊢ ( ( ( 𝜑 ∧ 𝜏 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )