Theorem 3adantr2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005)

	Ref	Expression
Hypothesis	3adantr.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion	3adantr2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜏 ∧ 𝜒 ) ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3adantr.1	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
2		3simpb	⊢ ( ( 𝜓 ∧ 𝜏 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) )
3	2 1	sylan2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜏 ∧ 𝜒 ) ) → 𝜃 )